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# Set Theory - Science topic

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Publications related to Set Theory (10,000)

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The paper investigates from a proof-theoretic perspective various noncontractive logical systems, which circumvent logical and semantic paradoxes. Until recently, such systems only displayed additive quantifiers (Grišin, Cantini). Systems with multiplicative quantifers were also proposed in the 2010s (Zardini), but they
turned out to be inconsisten...

The Isabelle Higher-order Tarski–Grothendieck object logic includes in its foundations both higher-order logic and set theory, which allows importing the libraries of Isabelle/HOL and Isabelle/Mizar. The two libraries, however, define all the basic concepts independently, which means that the results in the two are disconnected. In this paper, we a...

Starting from a model with a Laver-indestructible supercompact cardinal κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}, we construct a model o...

Eskiden de böyleydi, şimdi de öyle! Her asırda, her coğrafyada, her zaman ve her yerde siyaset böyle bir şey: yalan/dolan, kandırma/aldatma, kayırma/kollama, istismar/suistimal… Siyasetçi kimliği de bir o kadar kötü: seviyesiz/tıynetsiz, hayasız/haysiyetsiz, habis/haris, pespaye ve tam anlamıyla rezil ü rüsva… Antik Yunan ve Antik Roma’dan, Machiav...

In this paper, we address two problems proposed by Arhangel'skii. In Solution 2, we demonstrate that it is possible to construct a weakly first-countable compact space X such that |X| > 2 ω , where 2 ω represents the cardinality of the continuum. The construction is based on the ordinal space [0, ω1) with the order topology, where ω1 is the first u...

This paper explores the relationship between Lindelöf spaces and G δ-points. Specifically, we investigate whether the cardinality of a Lindelöf space with G δ-points is bounded by 2ω, where ω represents the cardinality of the set of natural numbers. Through rigorous analysis and counterexamples , we demonstrate that this cardinality restriction doe...

A bijective analysis is confirming, the expansion of universal space has never been directly observed, and this assumption is unproven thus far. The measurement of the gravitational redshift, which was confirmed using the Mossbauer experiment, proves only the gravitational redshift and nothing more because there is no causality between the gravitat...

We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that collapse 2ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag...

Frucht's theorem is the statement that "every group is the automorphism group of a graph". This was shown over ZFC independently by Sabidussi and deGroot, by induction using a well ordered generating set for the group. Sabidussi's proof is easily modified to use induction on the rank of a generating set, and thus holds over ZF. We show that Frucht'...

La Filosofía nunca ha sido un ejercicio de pensamiento dogmático, y la obra de Alain Badiou no es la excepción, pues ya es sujeto de debates contemporáneos planteados por Mehdi Belhaj Kacem, Slavoj Žižek, Jacques Rancière, Barbara Cassin, Elizabeth Roudinesco. Los problemas filosóficos que distingue la obra de Badiou y el corpus de sus intérpretes,...

There is no single canonical polynomial-time version of the Axiom of Choice (AC); several statements of AC that are equivalent in Zermelo-Fraenkel (ZF) set theory are already inequivalent from a constructive point of view, and are similarly inequivalent from a complexity-theoretic point of view. In this paper we show that many classical formulation...

This paper attempts to look at Fightbooks as literary sources and apply this reasoning to ADVISE reconstruction methodology. First the concepts of Real and Imaginary Worlds is introduced, followed by the distinction between Actors and Roles. Based on descriptions each Actor and Role can be assigned a set of Actions, Decisions, Intentions and Goals...

We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal interpretation. It also for the first time embeds a large common-sense ontology into a very secure interactive theorem p...

The “dual-carbon” policy underscores the crucial importance of a secure and stable natural gas supply to ensure the reliable operation of power systems. In high-load areas with a high proportion of gas-fired units and no alternative energy supply, urgent attention needs to be paid to the impact of natural gas loss on power system reliability. Given...

Robots that operate in real-world settings must be able to recognize, model, and infer the semantic features of things. Existing frameworks for knowledge reasoning are only able to describe the binary relationships between the semantic qualities of an item and its class label; they are unable to reason about the attributes of objects that are ident...

This note addresses the continuum problem, taking advantage of the breakthrough mentioned in the subtitle, and relating it to many recent advances occurring in set theory.

This work investigates the short-term dynamics caused by shape changes of morphing aircraft. We select a symmetric variable sweep morphing aircraft as the object of study and establish a six-degree-of-freedom multi-loop cascade model, and the coupling between derivative terms is eliminated by matrix transformation. Considering that the change in ae...

Under the background of the water crisis, there has been much research on corporate water responsibility (CWR), a subfield of corporate environmental responsibility (CER). Studies on CWR and CER are mainly focused on isolated factors, such as institutional pressure, corporate features, and managerial perceptions, with a notable lack of consensus. T...

We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a concept of pure data, which is used to represent all mathematical objects. As an axiomatic system, the foundation...

With this study, we perform a systematic and critical review of the studies conducted with the QCA, a set-theoretic approach, in tourism literature. Initially, we present the state of the art of QCA and a short guide for researchers with a process chart. Afterward, we identify the QCA studies in tourism and performed the bibliometric analysis with...

In an organization, successful implementation of Total Quality Management (TQM) brings lot of benefits in terms of quality improvement, customer satisfaction, profit, and market share. It also assists businesses to improve in terms of performance, reducing rework in the process, and reduction in overall costs associated with poor quality (e.g. repl...

The quest for complete observables in general relativity has been a longstanding open problem. We employ methods from descriptive set theory to show that no complete observable is Borel definable. In fact, we show that it is consistent with the Zermelo-Fraenkel and Dependent Choice axioms that no complete observable exists whatsoever. In a nutshell...

As climate continues to change, severe weather events continue to increase in both severity and frequency. The U.S. National Weather Service (NWS) established storm prediction centers around the country to monitor and produce predictions, warnings, and watches about weather events. However, the NWS relies mostly on local television stations to comm...

In order to scientifically and rationally assess the safety condition of coal mine production logistics system, this paper establishes a risk assessment model of coal mine production logistics system based on BWM-Vague set. On the basis of reviewing a large amount of literature and combining the main contributing factors of coal mine production saf...

Election is as a result, one of the cardinal features of democracy, which however, is constantly assaulted through the phenomenon of vote racketeering. The study examined Owerri resident's perception of the influence of radio sensitization programme against vote racketeering towards the 2023 Presidential election in Nigeria. The investigation was a...

The concept of single-valued neutrosophic sets (SVNSs) is considered as an attractive tool for dealing with highly ambiguous and uncertain information. The correlation coefficient of SVNSs acts as an important measure in the single-valued neutrosophic set theory and it has been applied in various fields, such as the pattern recognition, medical dia...

Der Beitrag vertieft das Verständnis die mathematische Unendlichkeit zu quantifizieren. Offene und abgeschlossene Mengen erweisen sich als nicht haltbar. Die korrekte Verwendung der Bijektion macht einige Ergebnisse obsolet, die auf dem Mächtigkeitsbegriff beruhen. Elemente unendlicher Mengen werden neu gezählt. Die Fueter-Pólya-Vermutung ist zu ko...

This paper deepens the understanding of quantifying mathematical infinity. Open and closed sets turn out to be not tenable. The correct usage of bijections makes results obsolete based on the concept of cardinality. Elements of infinite sets are counted in a novel way. The Fueter-Pólya conjecture must be corrected. The fundamental theorem of set th...

From classical mechanics, in particular the motion in a straight line, together set theory and ordinal number theory, we prove a not-classical behaviour, a discontinuous motion and emission.

Random permutation set theory (RPST), as an uncertainty modeling approach considering underlying ordered information, is proposed based on permutation set recently. Different from Dempster–Shafer Theory (DST), RPST extends the event space from power sets to permutation sets and thus can distinguish weights between ordered sets of the same cardinali...

The paper sets out to evaluate and appraise the roles of mass media and press freedom in the process of democratic consolidation in Nigeria’s Fourth Republic (1999-2019); and the nexus between mass media, press freedom and democracy. In addition, the paper discusses the conceptual meaning of mass media, press freedom, democracy and democratic conso...

The main objective of this paper is the definition of a membership function assignment procedure based on inherent features of linguistic terms to determine their semantics when they are used for preference modelling. For this purpose, we consider what linguists say about concepts such as language complementarity, the influence of context, or the e...

Purpose: The aim of this study is to examine the effect of competence, whistleblower, and probity audit on the detection of fraud in the procurement of goods and services, with emotional intelligence as a moderator.. Theoretical framework: The theory used in this study to derive hypotheses is based on the Agency Theory and Goal Setting Theory. Agen...

Gatekeeping theory captures the process of sieving, shaping and reducing media contents into the few conveyed to the audience by a gatekeeper. This is necessary because the quantum of information generated by media workers and other media content sources often exceed the available space and air time. The gatekeeper is guided by timing, ownership pa...

This is a short introductory course to Set Theory and Category Theory, based on axioms of von Neumann--Bernays--Godel (briefly NBG). The text can be used as a base for a lecture course in Foundations of Mathematics, and contains a reasonable minimum which a good (post-graduate) student in Mathematics should know about foundations of this science.

The subject of this study is the process of engineering and geodetic surveys for developing road projects. The purpose of this article is to improve the efficiency of the process of engineering and geodetic research in road design by implementing remote data from various sources and their systematization and algorithmization of use. The task is to...

Despite its unparalleled success, quantum mechanics (QM) is an incomplete theory of nature. Longstanding concerns regarding its mathematical foundations and physical interpretation persist, a full century beyond its conception. Limited by these issues, efforts to move beyond QM have struggled to gain traction within the broader physics community. O...

Mathematics and Music are closely connected and their multifaceted relationship has been explored since ancient times. Pythagoras was one of the first who discovered and formalized one of those connections by studying the arithmetic of musical intervals, expressing them by numerical ratios and relating ratios to consonance/dissonance notions, being...

This article examines Hilbert spaces constructed from sets whose existence is incompatible with the Countable Axiom of Choice (CC). Our point of view is twofold: (1) We examine what can and cannot be said about Hilbert spaces and operators on them in ZF set theory without any assumptions of Choice axioms, even the CC. (2) We view Hilbert spaces as...

We present recent results on the model companions of set theory, placing them in the context of a current debate in the philosophy of mathematics. We start by describing the dependence of the notion of model companionship on the signature, and then we analyze this dependence in the specific case of set theory. We argue that the most natural model c...

A MATHEMATICAL MODEL is presented to define new inclusions, intersections and unions as alternatives to the usual ones between crisp and fuzzy subsets. In particular, the concept of “the non-trivial content of the empty set ∅” is analyzed.
This proposed model is based on the interconnection of two consolidated mathematical concepts in specialized...

A structural analysis of construction schemes is developed. That analysis is used to give simple and new constructions of combinatorial objects which have been of interest to set theorists and topologists. We then continue the study of capturing axioms associated to construction schemes. From them, we deduce the existence of several uncountable str...

The purpose of resource scheduling is to deal with all kinds of unexpected events that may occur in life, such as fire, traffic jam, earthquake and other emergencies, and the scheduling algorithm is one of the key factors affecting the intelligent scheduling system. In the traditional resource scheduling system, because of the slow decision-making,...

Perceptions of an East–West divide in the European Union (EU) with regard to democracy have led to re-evaluations of EU eastern enlargement as a policy failure and militate against further enlargement. This article examines the accuracy of narratives of an intra-EU East–West divide on democracy, in which the western member states outperform the eas...

Alain Badiou adalah salah satu filsuf yang terpengaruh pemikiran Marxisme. Melalui matematika, Badiou mencoba menjelaskan kondisi sosial-politik masyarakat dalam bingkai Marxisme. Bagi Badiou, di dalam masyarakat selalu ada komponen yang tidak terwakili meskipun ada di dalam masyarakat. Komponen tersebut menjadi tidak terwakili karena tidak terhitu...

Environmental cues (e.g. achievement-related words and
pictures) can prime/activate, in the absence of awareness, a
mental representation of importance stored in memory. Chen
et al.’s 2021 Applied Psychology: An International Review 70,
216–253. (doi:10.1111/apps.12239) meta-analysis revealed a
moderate, significant overall effect for the goal prim...

This paper proposes a novel distributed coverage controller for a multi-agent system with constant-speed unicycle robots (CSUR). The work is motivated by the limitation of the conventional method that does not ensure the satisfaction of hard state- and input-dependent constraints and leads to feasibility issues for multi-CSUR systems. In this paper...

In the lecture notes it is shown that an ordinal $\psi_{\Omega}(\varepsilon_{\mathbb{S}^{+}+1})$ is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}\omega+(M\prec_{\Sigma_{1}}V)$. In this note we show that ${\sf KP}\omega+(M\prec_{\Sigma_{1}}V)$ proves the well-foundedness up to $\psi_{\Omega}(\omega_{n}(\mathbb{S}^{+}+1))$...

We present the first section (theorems 4 to 100) of our PyLog formalisation of Set Theory as presented in the famous appendix of Kelley's General Topology[4].

A bijective analysis is confirming, the expansion of universal space has never been directly observed, and this assumption is unproven thus far. The measurement of the gravitational redshift, which was confirmed using the Mossbauer experiment, proves only the gravitational redshift and nothing more because there is no causality between the gravitat...

appeared, soft set theory grew at a breakneck pace. Several authors have introduced various operations, relations, results, etc. as well as other aspects in soft set theory and hybrid structures incorrectly, despite their widespread use in mathematics and allied areas. In his paper [Molodtsov D. A. Equivalence and correct operations for soft sets,...

The logical model labelled "Zone-Theory", borrowing from the mathematics of Set Theory, seeks to give firmer foundations to theoretical physics as well as to solve the so-called "Problem of Time". Indeed, in the scientific search for a “Theory of Everything” (a theory unifying mathematically Quantum Mechanics and General Relativity), one of the cor...

A bijective analysis is confirming, the expansion of universal space has never been directly observed, and this assumption is unproven thus far. The measurement of the gravitational redshift, which was confirmed using the Mossbauer experiment, proves only the gravitational redshift and nothing more because there is no causality between the gravitat...

This study presents fundamental theorems, lemmas, and mapping definitions. There are three types of mappings: binary operators, compatible mappings, and sequentially continuous mappings. The symbols used to represent fuzzy metric spaces are intuitive. Icons were also used to prescribe a shared, linked fixed point in intuitionistic fuzzy metric spac...

Nowadays, several fuzzy extensions of ELECTRE (Elimination and Selection Transforming Reality) and TOPSIS (The Order Preference by Similarity to Positive Ideal Solution) methods are emerging as powerful mathematical tools for dealing with uncertainties in different multi-criteria decision-making (MCDM) situations of medical and engineering domains....

Causal set theory is a discrete model of spacetime that retains a notion of causal structure. We understand
how to construct causal sets that approximate a given spacetime, but most causal sets are not at all
manifold-like, and must be dynamically excluded if something like our universe is to emerge from the theory.
Here we show that the most com...

In a first-order theory $\varTheta $, the decision problem for a class of formulae $\varPhi $ is solvable if there is an algorithmic procedure that can assess whether or not the existential closure $\varphi ^{\exists }$ of $\varphi $ belongs to $\varTheta $, for any $\varphi \in \varPhi $. In 1988, Parlamento and Policriti already showed how to tai...

The aim of the present study is to investigate the U.S. withdrawal from Afghanistan in the news coverage of Pakistani newspaper Dawn, U.S. newspaper New York Post and Afghanistan newspaper Afghanistan Times during the period 14th April to 31st August 2021 in accordance with their foreign policy.The purpose of the study how the newspapers of three m...

A vaga pedagógica do Movimento da Matemática Moderna (MMM) proporcionou, em terras brasileiras, transformações de elementos curriculares, metodológicos e didáticos no ensino da Matemática no período em que ocorreu, especialmente entre os anos de 1960-1970. Dito isso, novos saberes a ensinar foram incluídos no ensino da Matemática, sendo, um deles,...

Financial literacy is crucial to financial inclusion and facilitates access to and use of formal financial services and products. This study aims to investigate the role of financial literacy in improving financial inclusion among Pakistan’s women (a country characterized by a high gender gap and lower financial inclusion). A positivist philosophy...

We examine what happens if we replace ZFC with a localistic/relativistic system, LZFC, whose central new axiom, denoted by $Loc({\rm ZFC})$, says that every set belongs to a transitive model of ZFC. LZFC consists of $Loc({\rm ZFC})$ plus some elementary axioms forming Basic Set Theory (BST). Some theoretical reasons for this shift of view are given...

Sería natural suponer que el espacio (o la espacialidad) como parámetro dentro de la música electroacústica puede ser considerado como algo intrínseco e inherente a casi cualquier obra que sea presentada en formato multicanal (y por supuesto, estéreo) debido a las cualidades, características y consecuencias acústicas y psicoacústicas derivadas de l...

The liver is an essential source of various vital proteins that specify the normal function of the blood coagulation cascade. Coagulation and abnormality in blood clotting levels are considered crucial indicators for many liver diseases such as cirrhosis and assess the liver injury and toxicity. However, detecting the coagulation degree of liver ti...

This dissertation aims to provide a comprehensive account of set theory with urelements. In Chapter 1, I present mathematical and philosophical motivations for studying urelement set theory and lay out the necessary technical preliminaries. Chapter 2 is devoted to the axiomatization of urelement set theory, where I introduce a hierarchy of axioms a...

This paper demonstrates that some non-classical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed in a survey affects whether p...

By a virtual model, we mean a model of set theory which is elementary in its transitive closure. Virtual models are first used by Neeman \cite{neeman2014forcing} to iterate forcing. That paper is concerned with proper forcing. The method was then adjusted by Veli\v{c}kovi\'c to the case of semi-proper forcing and this was drafted in \cite{velickovi...

We adjust the notion of typicality originated with Russell, which was introduced and studied in a previous paper for general first-order structures, to make it expressible in the language of set theory. The adopted definition of the class ${\rm NT}$ of nontypical sets comes out as a natural strengthening of Russell's initial definition, which emplo...

Ernst Zermelo's axiomatization of set theory (1908) did not exclude `a set that is a member of itself'. We call a set that is a member of itself `an individual'. In this article we prove the elimination of Russell's paradox is equivalent to "For every set S, an individual is a member of S or a set (but not an individual) is not a member of S". This...

The present paper attempts to modify the way of constructing a measure in the Alternative Set Theory setting originally devised by Martin Kalina. Introducing a system of cuts of rational numbers extended with some special ones, it is proved that the measure which is nondecreasing, nonnegative and "depending on the way of measurement" as same as Kal...

Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory, consistent or inconsistent, consists of truths about its own (possibly uninteresting) domain of individuals and relations; and (3) the principal philosophie...

Zero signifies absence or an amount of no measure. This mathematical object purportedly exemplifies one of humanity’s most splendid insights. Endorsement of the continuum consolidated zero as a cultural latecomer that, at present, everybody uses daily as an indispensable number. Zero and infinity represent symmetric and complementary concepts; why...

Deep learning models have been widely used in many supervised learning applications. However, these models suffer from overfitting due to various types of uncertainty with deteriorating performance when facing data biases, class imbalance, or noise propagation. The Information-Set Deep learning (ISDL) architectures with four variants are developed...

For more than a century, Cantor's theory of transfinite numbers has played a pivotal role in set theory, with ramifications that extend to many areas of mathematics. This article extends earlier findings with a fresh look at the critical facts of Cantor's theory: i) Cantor's widely renowned Diagonalization Argument (CDA) is fully refuted by a set o...

We mechanise the undecidability of various first-order axiom systems in Coq, employing the synthetic approach to computability underlying the growing Coq Library of Undecidability Proofs. Concretely, we cover both semantic and deductive entailment in fragments of Peano arithmetic (PA) as well as ZF and related finitary set theories, with their unde...

The celebrated geodesic congruence equation of Raychaudhuri, together with the resulting singularity theorems of Penrose and Hawking that it enabled, yield a highly general set of conditions under which a spacetime (or, more generically, a pseudo-Riemannian manifold) is expected to become geodesically incomplete. However, the proofs of these theore...

Microarray technology is an important innovation that simultaneously facilitates measuring the expression level for thousands of genes in different samples. One basic and widely used technique in microarray data analysis is clustering. Due to some characteristics of microarray data related to noise, redundancy, and complex biological hidden process...

A lane-change maneuver on a congested highway could be severely disruptive or even infeasible without the cooperation of neighboring cars. However, cooperation with other vehicles does not guarantee that the performed maneuver will not have a negative impact on traffic flow unless it is explicitly considered in the cooperative controller design. In...

The present study validly connects modern scientific research & the subjective truth. The rich Indian knowledge system’s ‘Chaitanyatma Research Levels Model’ is constitution of the manifest plus un-manifest Brahman in a single, reality based iconic infographic-The Shivalinga. By knowing the simplistic hierarchical model of creation & evolution in t...

The paper discusses the 2022 Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Paul...

After a seminar on new thinking in school mathematics held in Royaumont in 1959, four Nordic countries, Denmark, Finland, Norway, and Sweden, agreed to cooperate on school mathematics reform. A joint committee, the Nordic Committee for the Modernization of School Mathematics, declared a need for revising aims and content. Concepts from set theory,...

In this article, we show that every stationary random measure on R^d that is essentially free (i.e., has no symmetries a.s.) admits a point process as a factor. As a result, we improve the results of Last and Thorisson (2022) on the existence of a factor balancing allocation between ergodic pairs of stationary random measures Φ and Ψ with equal int...

The proposed paper describes the influence of woven fabric constructional parameters (type of weave, relative fabric density) and colouration (obtained by eco-friendly dyeing) on the solar transmittance of cotton woven fabrics in the range of 210–1200 nm. The cotton woven fabrics in their raw state were prepared according to Kienbaum’s setting theo...

It is necessary to emphasize both the process and results of performance management to find the balance between quality and quantity needed to ensure the sustainable development of universities to make the best use of limited educational resources and meet the diverse needs of students. This study applies failure mode and effects analysis (FMEA) to...

The Nigerian home video (Nollywood) phenomenon has reached a point of development where it can no longer be ignored. It is difficult now to find an average Nigerian who does not have an idea and opinion of Nollywood, whether positive, negative or non-committal. As is common knowledge, newspapers generally provide fora for acquiring and updating kno...

Starting from the mathematical definition of a pair in set theory, the author describes the get−go of universal expansion as a purely mathematical scenario. This preimage belongs to the Platonic world of ideas. According to the definition of the observer of the world as a set, besides a "null" assumption of the Platonic world of ideas being a (meta...

The assignment of feeling and meaning to the physical world is brought about by hierarchical categorical reference frames, anticipatory prediction, brain state feedback vetting cycles, and emergent renormalization; combined, these physiological processes are instrumental in the development of phenomenal awareness and all conscious thought. Specific...

The spate of communal conflicts in Nigeria has become a nightmare for citizens. In Benue State, the farmers/herdsmen conflict has become a cause of concern as armed herdsmen continue to openly graze, destroy crops, maim and kill citizens on daily basis despite the implementation of the Open Grazing Prohibition and Ranches Establishment Law in 2017...

This research examined the interplay among personal factors, namely channel lock-in, cross-channel synergy, attribute-based decision making (ADM); environmental factors, namely others’ past switching behaviour (OPB), pressure to switch from others (PSO); and behavioural factors, namely perceived self-efficacy and perception on facilitating conditio...

The 2022 Tel Aviv conference on the many-worlds interpretation of quantum mechanics highlighted many differences between theorists. A very significant dichotomy is between Everettian fission (splitting) and Saunders–Wallace–Wilson divergence. For fission, an observer may have multiple futures, whereas for divergence they always have a single future...