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SPIRAL cosmological redshift hypothesis and cosmology model in theory does not require hyper-dense proto stellar formation, just that the proto-stars existed by he cosmic inflation expansion event. However from my limited perspective the natural observations align best with proto-stellar formation being hyper-dense with a proportional expansion, during a /the cosmic inflation expansion event, hypothesized in SPIRAL..
So assume SPIRAL and hyper-dense proto stellar formation.
How could the scientific process have worked if this is the actuality?
What factual natural observations appear to align with this?
What if any factual natural observations might precluded this?
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Pearlman SPIRAL electro-magnetic repulsion, HTP early proto galactic formation and even black-hole illusion resolution align best with and are being confirmed by JWST
A recent article:
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Successful Factors on the trade managements
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rade show management models are a set of theories and frameworks that describe the key elements and processes involved in planning, organizing, and managing trade shows. These models help trade show organizers understand the various stages and tasks involved in managing a successful trade show and provide guidance on best practices for each stage.
One commonly used trade show management model is the event management cycle, which consists of five stages: planning, design, coordination, implementation, and evaluation. The planning stage involves defining the objectives of the trade show, identifying the target audience, and developing a budget and timeline. The design stage involves creating a layout and floor plan, selecting vendors and exhibitors, and creating marketing materials. The coordination stage involves managing logistics, such as transportation, accommodations, and staffing. The implementation stage involves setting up the trade show and managing the event itself, including registration, security, and on-site support. Finally, the evaluation stage involves assessing the success of the trade show and identifying areas for improvement.
Another trade show management model is the stakeholder model, which focuses on identifying and managing the interests and needs of different stakeholders involved in the trade show, such as exhibitors, attendees, sponsors, and vendors. The model emphasizes the importance of building relationships with stakeholders and developing strategies to meet their needs and expectations.
Overall, trade show management models provide a framework for understanding the complex processes involved in managing a successful trade show and can help organizers develop effective strategies and practices for each stage of the event.
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This is a question about Godel Numbering. As I understand it, the axioms of a system are mapped to a set of composite numbers. Is this really the case, so for example the 5 axioms of Euclidean plane geometry are mapped to 5 composite numbers? Does this also imply that theorems of the system are now composite numbers that are dependent on the composite numbers that were the target of the map from the set of axioms PLUS the elementary numbers that describe the logical operations, such as +, if..then, There exists, ext.?
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From what I understand, you are asking whether it is sensible to investigate the nature of numbers coding axioms (finitely many) of a given theory, or more generally, study a formal theory with respect to its coding and see whether it is possible to "extrapolate" from theorems provable in this theory a number representing a code of a formulation of an axiom. It has already been said that the Gödel numbering used in the proof of the Incompleteness theorem is canonical and probably given its computational inefficiency maybe also inadequate for this particular question (again, assuming that I understood your question correctly).
However, the main idea of understanding how theorems are, in some sense, computationally linked to the premises which entail them is a very interesting question. It is clear that the possibility of arithmetizing a formal theory enables to provide a number theoretical interpretation to the objects of a formal theory (syntax, semantics and proof theory). In this sense, one could ask whether it is possible to find a "preferable" coding for a formal theory in order to make your question easier to formulate and answer. This is of course extremely vague, but to make things more precise, you could try to pick a specific theory (Euclidean Geometry), formalise the axioms and define different codings and see whether, with respect to what you are trying to investigate, it is possible to establish how a particular choice of coding affects the nature of the numbers coding your axioms.
Finally, I wanted to conclude by referring to a recent program in mathematical logic called Reverse Mathematics. They are basically trying to isolate axioms from theorems (which is some sense related to the remark you made "[..]going in the other direction, starting with a result in number theory and then try to conclude something about formal systems or axioms.") and they actually use a lot of computability theory and subsystems of second-order arithmetic. I am not an expert on this particular topic, but I suggest you to look into it if you are interested.
I would be happy to carry on this discussion with you and also, if during the past year you obtained some interesting results that you can share, I would be glad to hear them.
Thank you and best regards!
Jean Paul Schemeil
Links for Reverse Mathematics:
Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689
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In the 21st century, we can safely say that absolutely all modern achievements in the field of science are based on the successes of modeling theory, on the basis of which practical recommendations are given that are useful in physics, technology, biology, sociology, etc., are extracted. In addition, this is due to the fact that the application of the principles of the theory of measurements in determining the fundamental constants allows us to check the consistency and correctness of the basic physical theories. In addition to the above, the quantitative predictions of the main physical theories depend on the numerical values ​​of the constants included in these theories: each new sign can lead to the detection of a previously unknown inconsistency or, conversely, can eliminate the existing inconsistency in our description of the physical world. At the same time, scientists have come to a clear understanding of the limitations of our efforts to achieve very high measurement accuracy.
The very act of measurement already presupposes the presence of a physical and mathematical model that describes the phenomenon under study. Simulation theory focuses on the process of measuring the experimental determination of values ​​using special equipment called measuring instruments. This theory covers only aspects of data analysis and the procedure for measuring the observed quantity or after the formulation of a mathematical model. Thus, the problem of uncertainty before experimental or computer simulations caused by the limited number of quantities recorded in the mathematical model is usually ignored in measurement theory.
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interesting discussion
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I was wondering is there any
  • model theory of number theory ,hence are there model theorists working in number theory
  • the development of arithmatic geometry ,does it have anything to do with questions in logic;and is there any group studying this interaction.
  • Anyone is welcome and up for collaboration
  • I am interested in finding interaction between algerraic and arithmatic number theory with logic,and to study it to answer logical questions about Arithmatic
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As far as I know, in the entire history of mankind, only two philosophers have seriously dealt with logic, this is Aristotle and Hegel. Of these, only Hegel did mathematics. Nobody else dealt with this problem.
Sincerely, Alexander
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Hi, is anyone familiar with a model/theory of memory recall and recognition in math education? Thank you
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For a start, try George Mandler's 1980 article in Psychological Review entitled Recognizing: The Judgment of Previous Occurrence.
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I would appreciate if you can suggest an model/theory would best fit for investigating the availability of government information and e-services and its impact to the users' economic benefits/growth except SERVQUEL/TAM. Your valuable suggestions and sharing relevant resources would be a great contribution.
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Thank you dear Prof. Desalegn Abraha Gebrekidan
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I want to investigate if delivery of government information and e-services delivery will have any effects on rural people economic growth / benefits in the least developed / developing countries context. Any model / theories / papers to recommend, please?
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Thanks dear @,Muhammad Ali.
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I have behavioral data (feeding latency) which is the dependent variable. There are 4 populations from which the behavioral data is collected. So population becomes a random effect. I have various environmental parameters like dissolved oxygen, water velocity, temperature, fish diversity index, habitat complexity etc. as the independent variables (continuous). I want to see which of these variables or combination of variables will have significant effect on the behavior.
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I agreed with Abdullahi Ubale Usman answer. But some other techniques like non-linear analysis, cluster analysis, factor analysis, etc. may be utilized in this regard
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what are the key models and theories used to assess the CPD for teachers.
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The success of a CPD programme is dependent on the extent to which the packaging of content knowledge and curricula experiences are geared towards (1) translation of that knowledge in practice, and the (2) transformation of one's practices in the practice site.
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Dear all,
I am looking for a model or theory, which deals with general dimensions of technology (for example functional dimension, technical dimension, economical dimension).
Does anyone have recommendations?
Thank you very much for all suggestions and help!
Best regards from Germany,
Katharina Dröge
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You got a very large domain to study. I think you should be prepared to:
1. decide over the research domain to be divided into simple pieces;
2. research the simple pieces by (formal) language and concepts, in parallel with modelling; I think the language and concept theories and UML will be very helpful here;
3. demonstrate the identity of results in 1 and 2;
4. imagine your abstract object - the technology of artificial intelligence; create a prototype to demonstrate your research method.
5. refer to 4, construct the configuration model;
6. research for design of your final goal.
7. think on how you can best transmit your results to the audience. If you got success here, then your results are most probable correct.
Hope the above to be of help in your attempt. Success!
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Hi,
I've heard that TA can be used to generate a model/theory from the data, similar to grounded theory, but none of the TA sources I've gone through state anything related to this claim. Does anyone know if the claim is true? If so, are there any sources that explain the process in detail or to any degree?
Thanks!
- Tez
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Thank you Dean, David, and Bahram. You've made the decision to stick with Gt much easier. Best of luck in all your endeavors. Cheers,
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The independence property is defined by Shelah. I am looking for other versions or generalization of the definition in which some circumstances are changed.
Main reference (p.316, Def. 4.1):
Shelah, S. "Stability, the f.c.p. and superstability." Ann. Math. Logic 3, 271–362 (1971)
Another reference: (First Def. in introduction)
Gurevich, Yuri, and Peter H. Schmitt. "The theory of ordered abelian groups does not have the independence property." Transactions of the American Mathematical Society 284.1 (1984): 171-182.
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Can you add a reference to the definition you have in mind?
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I am interested in published guidance or worked examples on how to analyse and synthesize existing theories, models and frameworks.
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Hi Lisa Pfadenhauer, not sure of the specific scope of your interest but I hope this excellent paper is relevant and of interest.
Nilsen, P. (2015). Making sense of implementation theories, models and frameworks. Implementation science, 10(1), 53.
Regards
Scott
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From the literature review, a model has been developed which is a new mechanism for poverty alleviation. I want to use grounded theory methodology research approach to establish a general theory through interviewing the stakeholders of the model.
I would appreciate if anyone answer how grounded theory methods I will adopt in this case.
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Grounded theory doesn’t use prespecified models. Instead it literally develops theory from the ground up. Thus the goal is to discover theory rather than to test it.
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Psihologija (www.psihologijajournal.org.rs) is a scholarly open access, no fee, peer-reviewed journal published quarterly. It is currently referenced in the Social Sciences Citation Index (SSCI).
As a journal mainly focusing on psychology, neuroscience and psychiatry, Psihologija calls for papers related to all aspects of Internet, digital media, smartphones and other technology use that could lead to potentially detrimental mental health effects. Original research and review articles about specific models and theories, definition, classification, assessment, epidemiology, co-morbidity and treatment options, focusing mainly on, although not limited to:
· Internet gaming
· Internet gambling
· Excessive social media/networks use
· Online dating, cyber-relationships/sex and pornography
· Excessive online information collection
· Cyberbullying
· Smartphones, tablets and other technology use.
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Giovanni Portuesi & Duane A Lundervold great! Definitely good articles are needed! Will be happy to provide more details if needed!
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The Theory Wiki at IS.TheorizeIt.Org gets over 200,000 visits annually, but is due for a bit of an update. If you publish on this theory, we would love your updates.
Kai :-)
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Hi Talita
Thank you for sharing your work. I am going to use TAM in combination with the adaptive structuration theory in a qualitative approach (case study/action research).
Regards
Roland
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a model or theory that will guide by mphil thesis. the topic is "lived experiences of parents of children with cancer"
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You can look at our paper and see if it gives you some ideas:
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the basic theory of this Model is theory of social behavior
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Have you seen this? It is also addressed to children with social barriers:
Greetings to Indonesia.
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" I dont know about the innovation so i dont use it, if i know about it i'll use the innovation"
i've been getting that quite a lot when doing my research, my question, is there any theory about lacking of information in adoption technology? Please let me know if there any journal or book that i can read
thanks
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Hi Michael,
I have a classic to indicate. It is the book “Diffusion of Innovations Theory” by Everett M. Rogers. It offers a framework with some of the factors that may contribute to an innovation's success or failure.
He defined diffusion as “the process by which an innovation is communicated through certain channels over time among the members of a social system”. His work was wildly influential.
Rogers began his research by studying the mechanisms by which American farmers successfully adopted the agricultural innovations developed at universities. In a series of studies across multiple areas, he found that innovations that have 5 characteristics:
1. Relative Advantage: the degree to which an innovation appears to be better than any other alternatives the potential adopter might have, measured in terms of economics, convenience, satisfaction, and social prestige.
2. Trialability: the degree in which the innovation can be experienced firsthand on a limited basis.
3. Observability: the degree in which the innovation or its results can be seen by others likely to adopt it.
4. Compatibility: the degree to which the innovation is seen as consistent with existing values, previous experiences, and needs of the user.
5. Complexity: the degree in which the innovation is seen as difficult to understand or use.
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Population Simulation Problem: I need someone to collaborate in writing a population simulation program incorporating kinship rules of endogamy/exogamy, mating rules, territory and carrying capacity.
I am an evolutionary sociologist and author of a new multi-species population theory, which I can demonstrate in diagrams (also published in books). I want to have it expressed mathematically but need help for this.
Then I want help to model this theory, simulating populations, to show how different kinship and marriage rules, responsive to local environmental feedback, produce different fertility opportunities, beyond the predator/prey/density models, but I cannot write programs.
So, I need someone to add to an extant population simulation program or write a new one, so that I will be able to run variations myself. I would acknowledge the program writer as a contributor to the theory.
This could be a good new thesis basis for a program writer and life-sciences grad. Our work would need to be confidential prior to publication. Maybe more than one person could be involved. I welcome any advice as to what would be necessary.
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Thank you very much for this, Hamit. I still have to read it but I can see its relevance and research. I may have some questions.
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I am looking for recent subjects in the area of using Markov chains in queueing models or theory for the thesis of a master student in mathematics.
Thanks a lot in advance.
Mohamed I Riffi
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these are real topics that my graduates have done in recent years
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what do you think is the best way of managing toxic employees in an organisation? kindly share your thoughts, recommended approaches, model, theory or etc.
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Nice theory folks, except your assuming a subordinate or parallel toxicity whereas it might be the boss, director or so that may be a total social psychopath! Deal with them and see how far you get!
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I am trying to simulate diesel spray injection in constant volume chamber. I am using 2D axi-symmetric model with DPM. I understand from atomizer model theory that injection pressure is essential to calculate injection velocity. But I am not able to specify the same.Additional information about defining conditions of continuous phase in DPM will also be helpful. Thanks in advance.
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Unfortunately , There is no other way to input the pressure in plain orifice atomizer in fluent as it seems. My suggestions is that ,try to change the flow rate by using pressure drop equation ( Bernoulli Equation) and check it. Otherwise you have to move on to Pressure swirl atomizer.
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Suggest me the Model that will me direct me in writing this project more persistently and clearly.
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You might consider a Knowledge, Attitudes, and Practices (KAP) approach.
Another alternative is Knowledge-Attitude-Behavior, which despite the similar sounding name, is rather different from KAP.
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When we talk about human comfort, we usually think of thermal comfort, and many good models for individual thermal comfort have been proposed.
So my confusion is “How to measure the individual olfactory comfort?”. Could you tell me some models or theory related to it?
Or what factors can affect individual olfactory comfort?
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Dear Pei-feng,
there are standardized methods for the assessment of odour qualities:
  • The European Standards EN 16841 Part 1 and Part 2 introduce the measured variable of percentage odour time, i.e. the frequency with which the recognition threshold in the ambient air is exceeded during a single measurement and odours are recognized beyond doubt, e.g. facility-specific odours. Intensity and hedonic odour tone in the field are also described as additional characteristic variables of an odour (VDI 3940 Part 3). The determined intensity and hedonic odour tone of a facility-specific odour can serve as a guide to the estimation of the degree of nuisance.
  • Sensory testing of indoor air and the determination of odour emissions from building products using test chambers is specified in the international standards ISO 16000-30 and ISO 16000-28, respectively.
Best,
Sascha
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In order to start going into the topic, let us consider two alternatives. If we think that the photon dies out when absorbed then there is not much to talk about. However, if we consider the second alternative, lets us point out that in loosing its energy it becomes unobservable since our senses as well as all our apparatus need an energy transfer to achieve any detection.
So, if photons do survive after being absorbed they thus became ghost photons, i.e. invisible. Evidently this is problematic. But let us not dismiss so fast.
Let us make an imperfect analogy between a photon and a spring. If the spring vibrates it has an oscillatory energy. If it transfers its oscillatory energy to an external material it looses its energy, but the spring is still alive, it has not disappeared. Well, if you see the photon as an oscillator then the analogy makes some sense.
Let us address now a still more controversial issue. Let us suppose that if the spring is not stressed it has no strain mass. But if it is vibrating it has then just energy without having mass, and this analogically applies to the photon.
Well, let now consider the case of a stressed spring that is vibrating. It has then mass and energy. Again, analogically this applies to massive elementary particles.
Why should we appeal to very complicated models and theories? Is it really worthy?
Those interested in this viewpoint and willing to go deeper into this issue may read the paper: “Space, this great unknown”, available at: https://www.researchgate.net/publication/301585930_Space_this_great_unknown
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Dear Daniel.
How much credibility can we grant to theoretical physics?
It looks like you prefer to rely on the conventional theoretical physics, however the image that theorists are giving is not that much upright. Let me illustrate this.
In December 2015 an excess at 3.6 local sigmas was observed at 750 GeV in the difotonic channel (H → γγ), by pure chance, both in ATLAS and CMS (LCMF, Dec 15, 2015). This led to the publication of more than 600 theoretical articles in arXiv about the process (LCMF, Mar 22, 2016). Months later the excess disappeared (LCMF, 05 Aug 2016).
So, in a few months 600 theoretical articles were written justifying a fake event. What is therefore the credibility of mathematical issues in view that they can manage to justify an inexistent upshot?
Theorists should be more careful in “not throwing so many stones against the roof of their house”. Furthermore, “Publish or perish” may not be so wise after all and publishing compulsivity may have the opposite effect.
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i am trying to generate diffrent mppt algorithm for pv model using simulink. i am kinda lost even though i have the whole system is running. its just i am trying to test diffrent algorithms and compare the results.  could anyone help me showing simulink model or the theory behind it?
thanks    
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If you are working with MATLAB Simulink software then this video from the official channel of MATLAB can help you with implementation of three different MPPT algorithms in three different ways.
Modeling and Simulation of PV Solar Power Inverters- https://www.youtube.com/watch?v=GnZFi9CzF9Q 
For theory there are numerous papers and books already available.
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Study Related Material and some related research papers.
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It's worth going to the homepage of Icek Ajzen himself
And while no-one should regard Wikipedia as a strong authority on anything, the treatment there of this topic is pretty good.
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I have to do a presentation a model that is governed by distributed theory. I have to emphasize the real world implication of the model and the theory or theories that govern it.
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Does the professor permit you to ask other people for the answer rather than researching the answer on your own?
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Any models or theories used to identify the influence factors of counseling theoretical orientation.
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The work of Scott Miller, Ph.D. and colleagues has indicated that the theoretical orientation contributes only a small amount of variance compared to the relationship between the patient and therapist. David Kraus, Ph.D. has also published findings on the effectiveness of individual therapists vs. the theoretical approach used. 
The area that has not been sufficiently considered is whether certain characteristics of the patient would be associated with better outcomes with certain approaches than others. For example, would someone require encouragement for making changes do better with a motivational enhancement approach than CBT? Would someone with a substance use disorder and a lack of social network do better with a peer-support system such as 12-Step programs provide than MI or CBT? There have been some tantalizing indications that that might be the case, but there is a lack of dedication and sophistication in exploring differential results based on patient characteristics.
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I was looking for examples of first order sentences written in the language of fields, true in Q (field of rational numbers) and C (field of complex numbers) but false in R (field of real numbers). I found the following recipe to construct such sentences. Let a be a statement true in C but false in R and let b be a statement true in Q but false in R. Then the statement z = a \/ b is of course true in Q and C, but false in R. 
Using this method, I found the following z:=
(Ex x^2 = 2) ---> (Au Ev v^2 = u)
which formulated in english sounds as "If 2 has a square-root in the field, then all elements of the field have square roots in the field." Of course, in Q the premise is false, so the implication is true. In C both premise and conclusion are true, so the implication is true. In R, the premise is true and the conclusion false, so the implication is false. Bingo.
However, this example is just constructed and does not really contain too much mathematical enlightment. Do you know more interesting and more substantial (natural) examples? (from both logic and algebraic point of view)
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Something algebraic, implicitly talking about ordering:
"for every nonzero number x, x or -x is a square but not both."
This holds in R (it is essentially an axiom of real closed fields) but not in Q or C (x=2 is a counterexample for both). Now you can take the logical negation.
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The Baier and Katoen textbook references this paper
  • E. M. Clarke and I. A. Draghicescu. Expressibility results for linear-time and branching-time logics, pages 428–437. Springer Berlin Heidelberg, Berlin, Heidelberg, 1989.
to say that, given a CTL formula ϕ, if there exists an equivalent LTL one, it can be obtained by dropping all branch quantifiers (i.e. A and E) from ϕ.
The equivalence definition (from Baier & Katoen): CTL formula Φ and LTL formula φ (both over AP) are equivalent, denoted Φ ≡ φ, if for any transition system TS over AP:
TS |= Φ if and only if TS |= φ.
(Satisfaction |= is CTL or LTL respectively.)
Is there a syntactic criterion that provides a guarantee that if a CTL formula passes the test, then an equivalent LTL formula does exist?
Please note: Just dropping all branch quantifiers is not enough. For an example, consider 'AF AG p', where p is an atomic predicate. The LTL formula 'F G p' obtained by dropping the branch quantifiers is NOT equivalent to 'AF AG p', since it is not expressible in CTL. The question is whether there is a way (sufficient, but not necessary is Ok) of looking at a CTL formula and saying that it does have an equivalent LTL one?
I am emphasizing the need for a syntactic criterion, as opposed to the semantic one: drop the branch quantifiers and check the equivalence with the resulting formula. Something along the lines of: if, after pushing negations down to atomic predicates, all branch quantifiers are universal (A) and <some additional requirement>, then the formula has an equivalent LTL one (which, necessarily, can be obtained by dropping the branch quantifiers).
An additional requirement (or a totally different criterion) is necessary -- see the `AF AG p`.
Same question on CS Theory Stack Exchange (see the link)
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there is some work on the intersection of CTL and LTL:
The Common Fragment of CTL and LTL, Monika Maidl
The Common Fragment of ACTL and LTL, Mikolaj Bojan ́czyk ⋆
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What are the scientific basis and best acceptable modelling theory which exist prove projections of CC data and analysis of uncertainty analysis scientifically?
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There was a good paper on the uncertainty in CC forecast by Allen et al  in Nature:
Quantifying the uncertainty in forecasts of anthropogenic climate change
Nature 407, 617-620 (5 October 2000) | doi:10.1038/35036559
May be get started from there?
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Can  you  propose a model theory and basis set to be used in the computational studies of cyclic carbenes (cycloprpene carbene). Is it okay to apply to for both singlet and triplet states?
Thanks in advance.
Regards
Renjith Thomas
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First, research the literature so you won't double the existing papers. See e.g. http://www.sciencedirect.com/science/article/pii/S0166128099000329
Since your system is very small, you can go to very accurate methods (depending on available machines). Complete basis set calculations has been done 17 years ago (see the paper above) so now you should be able to do basically anything, including CCSDT or perhaps even G1-4.
You should definitely try both singlet an triplet, even if just to see if your methods of choice can reproduce experimental energy difference.
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I would like to know a good text on non-standard models of Peano arithmetic. And also, any article about then. Thanks. 
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Kossak and Schmerl: The structure of models of Peano Arithmetic.
Hajek and Putlak:  Metamathematics of First Order Arithmetic
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1. Surfactant molecule is made from water-loving head and grease-loving tail (Figure 1). My question: How do we measure the cross-sectional area of the alkyl chain of surfactant? Do we measure it vertically (refer to GREEN DOUBLE ARROWS of Figure 1) or horizontally (refer to RED DOUBLE ARROWS of Figure 1)? Or do we just take the “theoretical value" of the alkyl chain from the literature (estimated 20-25 A˚2)[1]?
2. I have read a paper entitled, "New Adsorption Model - Theory, Phenomena and New Concept - " by Shibata et. al. [2]. One of the sentences in para 3 page 2 stated that, i quoted, “The important finding is that molecular surface area is less than the cross-sectional area of the alkyl chain for C16E8 and C18E8. Such small molecular surface areas strongly suggest that Gibbs adsorption just at air/water interface in an adequate. This is one of contradictions for the Gibbs adsorption."
Why does when the molecular surface area is less than the cross-sectional area of the alkyl chain, it is said to be contradicted with the Gibbs adsorption?
Reference:
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Dear H. H. Mohammad: Surfactants having the same functional group in the solid layer have the same molecular area per one molecule. Functional groups may be different. In COOH 0.205 nm2. The area of 0.2 nm2 can be accepted for cross-sectional area of the alkyl group. Functional group -Cl, -F have a smaller cross-sectional area. Find a covalent radii and define the area. But if you are determined by the maximum adsorption monolayer, you will get a larger cross-section. Why? Answer yourselves.
Best regards
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Could contradiction play a role in quantum systems, as part of the mechanism of measurement, forcing a single random outcome from the spectrum of possibilities?
All ideas are welcome, including outrageous ones.
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My idea is that contradiction may be the impetus that forces decision during quantum measurement.  Again referring to the donkey dilemma  -- the donkey that starved to death after being placed equidistant between two bails of hay.  The donkey cannot feed because no preference is possible.
If the donkey was forced to move forward by some strict contradiction behind him, forcing a decision on him, the contradiction would be imperative while the non-preference is no imperative at all.  What do you think about this kind of idea?
Steve.
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In arithmetics or algebras that cannot be completed, if any statement is logically independent of the axioms, is it also mathematically undecidable.  Are these concepts identical?
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The difficulty is the multiple use of the word `undecidable'.   Here is some fairly standard notation.   1) A sentence phi is undecidable in  (or independent from) a theory T if both T union {phi} and T union {not phi} are consistent.
2) A theory T is decidable if its logical consequences form  a recursive set.
The easiest way to avoid confusion is to use only independent  from T and not undecidable in the first case.  1) is a property of a theory and sentence. 2) is a property of theory.
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Hello,
I am trying to write a chapter for my thesis about the most important models of economic growth, but somehow I can not figure out how to make a proper classification.
So far, I have this structure:
1. The classical theory of economic growth
a. Adam Smith theories
b. David Ricardo theories
c. Robert Malthus theories
2. Keynes theory of economic growth
3. Post-keynes theories of economic growth
a. Harrod-Domar model
4. Neoclassical theories of economic growth
a. Solow-Swan model
b. Ramsey - Cass - Koopmans model
5. New theories of economic growth (endogenous models)
a. Romer
b. Lucas
I fear that this classification is wrong and that I am not looking at the primary models/theories of economic growth. Can anybody guide me?
Kind regards,
Stefan
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Dear Stefan
Keynes theory of economic growth is based on models that are developed by Harrod-Domar and Kaldor for instance, while the Post-Keynesian theory is based on models that deal mostly with Sectors or Department such as developed by Marx and Sraffa. Both are different from the Neoclassical theory which took off with Robert Solow model. People who work on the Keynesian and Post-Keynesian models are at swords-point with Neoclassical theory as in the case of the "Cambridge Controversy on the Theory of Capital". Another difference is that Post-Keynesians and Keynesians are steep in Distribution and not only Growth theories. I think that you should keep them separate.
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I know that there is a model M for ZF such that. for an uncountable set S in this model and for every collection $\{ (X_s, d_s): s\in S\}$ of metric spaces in this model, their product $\prod_{s\in S} X_s$ in M is metrizable in M. In particular, for an uncountable set S in M, the product $\mathbb{R}^S$ is metrizable, however, I have not found this result in the literature so far. I would be grateful if you could tell me whether you have located  it in the literature. If your answer is YES,  please, tell me where I can find this result. I know how to prove the result. 
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Since some researches have asked  me via e-mail how I deduce that R^J can be metrizable for an uncountable set J in a model for ZF, let me give to all concerned the following theorem:
Theorem. Suppose that  a non-empty set J is a countable union of finite sets and that $\{ (X_j, d_j): j\in J\}$ is a collection of (quasi)- metric spaces. If each $X_j$ is equipped with the topology induced by d_j, then the product $\prod_{j\in J} X_j$ is (quasi)-metrizable. 
Now,  when M is a model for ZF+negation of CC(fin), there exists in M an uncountable set J such that J is a countable union of finite sets , so, for such a set J,   R^J is metrizable in M and, moreover, for example,  S^J is quasi-metrizable in M where S is the Sorgenfrey line. I was also surprised when I discovered these facts, They have looked strange in my opinion but they do not look strange now. They are relatively simple results. 
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Due to the specific way in which higher education is organized, any course of studies promotes the development of competences, which might seem, at first sight, beyond the grasp of didactics of higher education
I´m working on a model which depicts the development of students' competency in the intersection of didactics and organisation of higher educatio (see attachted file).
There are a lot of different theories for modelling and I´m not sure which one to choose best. Thank you!!!
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The theory model that is quite simple and versatile is Benner's Novice to Expert model. I use it as the basic competency development theory in my research into Field Dependent/Independent cognitive processing styles (Witkin, et al.). It has provided me with a curriculum development/assessment/evaluation framework in various educational settings.  dyerjean@gmail.com 
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In the semialgebraic context, Delfs and Knebusch defined in 1985 their "locally semialgebraic spaces" and later (only Knebusch) "weakly semialgebraic spaces" as some infinite gluings of semialgebraic spaces. But the majority of model theory seems to be carried out in Mn, where (M,...) is a structure (a kind of "affine" situation).
Do model theorists need to pass to infinite gluings from time to time?
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M^eq is not affine; it is an expansion of the vocabulary to guarantee that quotients are present. For definition of terminology see http://en.wikipedia.org/wiki/Imaginary_element
The examples there of `elimination of imaginary' are dull; more interesting is algebraically closed fields.
The compactness theorem is sometimes used to reduce infinite coverings to finite.  See for example Poizat's stable groups for the interaction between definable converings and algebraic geometry.
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Please can anyone help me with theories or suggest articles that help me understand why most countries used merger (amalgamation) system of banks as a suitable banking sector reforms. I am trying to synthesis the models used by my country’s former Central bank governor (Charles C. Soludo), in the banking reformation.
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To me Paul's answer talk is more related to the changes in environment than the models and theories. Further more BASE Regulations are not the drivers for M & E. The conventional theories of M&E are still applied. You should also look at the economic theories related to the scale and scope.
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I.  On Fri Oct 5 23:35:03 EDT 2007 Finnur Larusson  wrote
         I confirm that Larusson "proof"  under corrections can be formalized in ZFC.
II. On Sun Oct 7 14:12:37 EDT 2007 Timothy Y. Chow  wrote:
"In order to deduce "ZFC is inconsistent" from "ZFC |- ~con(ZFC)" one needs
something more than the consistency of ZFC, e.g., that ZFC has an
omega-model (i.e., a model in which the integers are the standard
integers).
To put it another way, why should we "believe" a statement just because
there's a ZFC-proof of it?  It's clear that if ZFC is inconsistent, then
we *won't* "believe" ZFC-proofs.  What's slightly more subtle is that the
mere consistency of ZFC isn't quite enough to get us to believe
arithmetical theorems of ZFC; we must also believe that these arithmetical
theorems are asserting something about the standard naturals.  It is
"conceivable" that ZFC might be consistent but that the only models it has
are those in which the integers are nonstandard, in which case we might
not "believe" an arithmetical statement such as "ZFC is inconsistent" even
if there is a ZFC-proof of it.
So you need to replace your initial statement that "we assume throughout
that ZFC is consistent" to "we assume throughout that ZFC has an
omega-model"; then you should see that your "paradox" dissipates.".
J.Foukzon.Remark1. Let Mst  be  an  omega-model  of  ZFC  and let ZFC[Mst]  be a  ZFC with a quantifiers bounded on model MstThen easy to see that  Larusson  "paradox"  valid inside  ZFC[Mst
III.  On Wed Oct 10 14:12:46 EDT 2007 Richard Heck wrote:
Or, more directly, what you need is reflection for ZFC: Bew_{ZFC}(A) -->
A. And that of course is not available in ZFC, by L"ob's theorem.
J.Foukzon.Remark2 However such reflection is .available in ZFC[Mst] by standard interpretation of Bew_{ZFC}(A) in omega-model  Mst    
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Remark4. However note thatthe condition of the existence standard model of ZFC    which has been requested  by T.Chow
is not necessary. It well known that any nonstandard model of FA (named MNst )  is necessary contains such minimal standard model of FA.see Theorem 3.1
Order-types of models of Peano arithmetic
MNst=N+AZ
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Is it possible to include repeated measures (permanent environment effect) inside the age(time) classes when utilizing random regression models?
The idea is trying to maintain the "time classes" interval length, so I won`t lose too much information in "not so big" data files.
Anyone have any experience with that?
Does that even have any support on random regression models theory?
Thanks in advance.
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Fair enough. I am interested in hearing how others with experience in this area respond.
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Looking for a model/theory/framework/ classic paper or systematic review that provides an overview on what factors influence a patient's decisions, in general and specific to treatment decisions?
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Chris, we are writing up a proposal and we were looking at different factors that influence patient's decisions as one factor: it seems as if most people keep directing to 'shared decision making' ideas however there must be other factors that influence a patient's decision. I am surprised that there is no overarching model or review on different factors ranging from socio-economic to shared-decision making to motivation....
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I am looking for a proof such that:
Given a set of Horn clauses, show that there is a unit refutation from S if and only if S is unsatisfiable
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Resolution, thus unit resolution, is sound. So the "only if" part is immediate.
At the ground level, the "if" part is really easy, but the trick at the first order level is showing that "factoring" is not needed. JACM 21,4 is overkill, but it does this amongst other results.
Intuitively, a ground positive unit proof can be lifted to (a proof of) the first order clauses, of which it is a set of instances, in the usual way -- EXCEPT that a single ground step may correspond to a unit resolution involving a clause in which k literals have been factored together into one. But unification theory allows this one step on a factor  to be replaced by k (unit) steps on the original clause, resulting in the same resolvent produced by the one step with the factor.
(This is mostly intuition and not even a proof sketch.)
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Besides Nursing Science Quarterly.
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Thank you
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I need to find an established definitions of Green Marketing and its antecedents.
Is there a model that can be used in understanding sustainability of Green marketing.
Thank you 
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Dear Colleague,
I would argue that the main theoriy supporting sustainability research is still  Stakeholder Theory  (Freeman, 1984, Carrol, 1979, MacWillims e Siegel, 2001, Carrol e Schwantz, 2003)   supporting the business case for social responsibility of organizations by focusing on the importance of a firm’s relationships with critical stakeholders that may lead to better performance, as organizations that integrate business and societal considerations create value for their stakeholders.
Another theoretical model that can support sustainability is  RBV- Resourced Based View Theory of the  Firm (Barney, 1991; Mac Williams e Siegal, 2001, Russo e Fouts, 1977) according to which VRIN (Valuable, Rare, Imperfectly imitable and Non-sustitutable), resources can produce competitive advantage and generate better operational results and sustainable results.
All the Best
Luis Fonseca
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In a formal arithmetical system, axiomatised under the field axioms, the square root of minus one is logically independent of axioms.  This is proved using Soundness and Completeness Theorems together. This arithmetic is incomplete and is therefore subject to Gödel's Incompletenss Theorems. But can it be said that the logical independence of the square root of minus one, is a consequence of incompleteness?
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The word "incompleteness" has meanings which are slightly different in the situations exposed.
Meaning 1: The axioms of fields do not define a complete theory. (Proof: both R (real numbers) and C (complete numbers)  are fields. Consider the formal statement  S: " exists x such that x2= - 1". R is a model of  "not A" and C is a model of A. Therefore, A is Independent of the deductive closure of the axioms of fields, so this set of sentences (sometimes called also "the theory of fields") is not complete.
Meaning 2: Gödel's Incompleteness Theorem says that any recurrent sets of axioms that are true for the ring of integers Z and is consistent, cannot be complete. [please put the accent on the word "recurrent"] Other said, the theory of Z is undecidable. This means that there is no one algorithm able to decide the truth or falsity (over Z) of all formal statements in the language of Z. (The same can be said for the set of natural numbers R, as Gödel originally did.)
IN CONCLUSION: The word "incompleteness" has very clear meanings in the two situations given in the question, but the two situations are so different, that no connection can be done, as suggested in the question.
HOWEVER: In the book Tarski - Mostowski - Robinson, Undecidable Theories, ways are shown how to interpret Gödel's incompleteness in order to show that some uncomplete sets of statements are also undecidable. Using those techniques they show that the deductive closure of group axioms is undecidable (there is no algorithms permitting us to decide if a formal sentence in the language of groups follows from the group axioms alone) and do the same thing with different theories of rings. I believe that the theoty of fields is in the same situation: not complete and undecidable. Maybe some experts will clarify this point in their posts.
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Nowadays, the consistency of theories is not demanded and in alternative we search for relative consistency. In the future things may change. In particular, in the answer 70 and more easily in answer 76, it was proved that set theory is consistent as a result of a relative consistency. There were published several datasets proving the consistency of set theory. In the last times it was publshed a paper in a journal, without success, since there is some inertia concerning the acceptance of the consistency of NFU set theory. It can be said that NFU set theory is consistent as the result of a relative consistency: since Peano arithmetic is consistent than NFU is consistent too. By a similar argument it can be prooved that set theory is consistent too: since NFU set theory is consistent then set theory is consistent. Thus, set theory is consistent, and since the related proof can be turned finite then we also prooved the Hilbert's Program, that was refered in many books on proof theory. There is an extension of set theory, the MK set theory, which is a joint foundation of set theory and category theory, two well known foundations of mathematics.  Once again a paper by myself with title "Conssitency of Set Theory" was rejected without a valid reason. This agrees with an answer given by me 26 days ago. With set theory consistent we can replace the use of models to prove the independence of axioms  (as did by Goedel and Cohen) by deduction in set theory.
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Zermello Fraenkel (ZF) and Zermello Fraenkel with Choice (ZFC) are only proposed Axiom systems. If they prove unconsistent, that does not mean that there are no sets, that there is no mathematics anymore, etc. This only means that a tentative of first order foundation by a system of schemes of axioms was unconsistent, and that the problem is open again. However, it is very likely that a new system of axioms set theory will most probably have the same problem as ZF: we will prove immediately that it is impossible to prove its consistency. So finally we will maybe adopt a position near to that of Bourbaki, in spite of its so called ignorance, see
To sum up: both if ZF is consistent or not, this question remains a never ending story by ist own and intimate nature. However, inspite of the possible instability of such an axiomatic construction, basic objects of mathematics like N, Q, R, C continue to exist and mathematics continue to be done. An incosistency of a given system of axioms does not touch the object for which it was standing. It touches only the problem of finding the right system of axioms for the given object.
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I want to scale down a 7m blade to a 0.30 m one as scaled down model then I want to study the dynamics and deflections under normal and tangential forces.
I work on using similitude theory such as using Buckingham Pi-theory and have some problems with using them.
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I didn't use it for real... so take this answer with precaution... But if it helps, lets try it.
For my part, I consider similitude studies as part of dimensional analysis, so the first step is to state what is the quantity you are interested in, and what are the influent (independent) parameters. For instance, if you are interested in deflection, u, consider that it is influenced by: the geometry (if the scale is respected, this collapses into a single size parameter, say L), the material (assuming linear elastic isotropic, two parameters, say Young modulus E, Poisson coefficient nu), the loading (normal force W, tangential force F)... and nothing more (this is the modeling part! If you forget something, the result will be false...)
Second, express the quantity of interest as an unknown function of the parameters, u=f(L,E,nu,W,F)
Then, if this function f is a physical law, it is independent of the choice of physical units. We can therefore select a dedicated choice. For instance, we can measure every length with L as a standard unit, and pressures with E. They are independent units. They are numerous enough for analysing statics (deflection), and we can check it by using the same physical law on values of each quantity in this new unit system (u is a length so it is measured with L, W is a force so it is measured with EL^2...), so:
u/L = f (L/L , E/E , nu , W/E/L^2 , F/E/L^2)
Note that the function f (unknown) is the same, nu as no unit, and that you found arguments with values 1=L/L=E/E that can be discarded. So
u/L = g(nu , W/E/L^2 , F/E/L^2)
Then you can add additional assumptions (not in the dimensional analysis theory! To be checked!). For instance that nu as small influence and you can neglect it, etc.
Then the physical law should be the same for the scaled model (subscript 1) and the real one (subscript 2) so
u1/L1 = g(nu1 , W1/E1/L1^2 , F1/E1/L1^2) and
u2/L2 = g(nu2 , W2/E2/L2^2 , F2/E2/L2^2) with the same unknown function g.
Now, imagine you measure something on the scaled model, say u1, you may predict u2 provided that you know the value of g for the specific arguments of the scaled model, i.e. if nu1=nu2, and W2/E2/L2^2 = W1/E1/L1^2, and F2/E2/L2^2 = F1/E1/L1^2 (similitude conditions) then
u2 = L2 x g(nu2 , W2/E2/L2^2 , F2/E2/L2^2) = L2 x g(nu1 , W1/E1/L1^2 , F1/E1/L1^2) = L2 x u1/L1
Hope this helps.
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By Godel's incompleteness theorem it is impossible to prove consistency of the current widely accepted foundation of mathematics ZFC within ZFC. But this theorem says nothing about existence or non-existence of a possible formal proof for inconsistency of ZFC within ZFC that means it is possible that some day set theorists or other working mathematicians find an inconsistency between two mathematical theorems.
My first question is about any possible option which could be chosen by set theorists, logicians and mathematicians in this imaginary situation.
Another question is about possible impacts of discovering an inconsistency in mathematics on philosophy of mathematics and some fields of human knowledge like theoretical physics which use mathematics extensively.
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It seems weakening the current axiomatic foundation of mathematics in any sense (including removing a particular axiom or moving to another weaker axiomatic system) causes an expected problem. In fact avoiding the contradiction by means of weakening our axiomatic system (which seems the only accessible choice) sends some accepted parts of current mathematics into the realm of "non-mathematics". Thus in this case we need to choose between different parts of mathematics that which one is good and useful and which one is not. This could be the matter of many discussions. For example if the Axiom of Choice (AC) is a part of that contradiction then by removing it from the foundation we will lose many useful tools of mathematics including many essential theorems like "Every vector space has a basis" that harms linear algebra extensively.
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Most textbooks on set theory comment on this possibility and the majority oppinion seems to be that if such inconsistencies would be discovered somewhere, it would probably be not too difficult to device some technical modifications (there are many modified axiomatic set theories in use already) that would avoid these inconsistencies (at the risk to introduce new ones, this would be a job guarantee for foundational mathematicians).
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I've proved the following theorem using model-theoretic techniques, namely ultraproducts: A continuum is locally connected if every semi-monotone mapping onto it (from another continuum) is monotone. Monotone means the usual thing; semi-monotone means that every subcontinuum K of the range space is the image of a subcontinuum in the domain space, which contains the pre-image of the interior of K. The part that uses ultraproducts is where we want to prove that non-locally connected implies being the image under a semi-monotone map that isn't monotone. Basically, I'm wondering if someone has any insights into obtaining a new proof more palatable to a continuum theorist. (E.g.: start with a non-locally connected metric continuum Y and directly construct a metric continuum X and a semi-monotone f:X->Y which is not monotone.)
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There are many incarnations of what is known as a continuum, e.g.,
1. continuum in set theory: the set R.
2. coninuum in topology: Hausdorff space. Distinct points belong to disjoint neighbourhoods.
I can suggest an approach in terms of a Hausdorff space. Let x and y be distinct points in a metric Hausdorff space X endowed with an Efremovic proximity relation. Let Nx, Ny be disjoint neighbourhoods of x, y, respective, where, for example,
\[
N_x = \left\{y\in X: d(x,y) < \varepsilon\right\},
\]
with $\varepsilon > 0$ and $d$ is the standard distance between x and y. Then Nx and Ny are connected, provided
\[
\mbox{cl}(A) \cap \mbox{cl}(B) \neq \emptyset.
\]
In other words, cl(Nx) and cl(Ny) have at least one point in common and cl(Nx) and cl(Ny) are then adjacent to each other. In other words, Nx and Ny are disjoint but cl(Nx) and cl(Ny) are not disjoint. If every pair of closures of disjoint neighbourhoods is connected in a subspace of X, then the subspace is locally connected.
One question to consider is this: what if Nx = {x} and Ny = {y}. Does the above line of reasoning work?