Conference PaperPDF Available

The double-incompleteness theorem

January 1976

Conference: Fourth All-Union Conference on Mathematical Logic
At: Kishinev

Authors:

Karlis Podnieks

University of Latvia

Let T be a strong enough theory, and M - its metatheory, both are consistent. Then there is a closed arithmetical formula H that is undecidable in T, but one cannot prove in M neither that H is T-unprovable, nor that H is T-unrefutable. For an English translation, see Section 6.2 of my book "What is Mathematics? Godel's Theorem and Around."

Content uploaded by Karlis Podnieks

Content may be subject to copyright.

Content uploaded by Karlis Podnieks

Content may be subject to copyright.

ResearchGate has not been able to resolve any citations for this publication.

ResearchGate has not been able to resolve any references for this publication.

Chapter

Circumference of a Circle (1932)

July 2014

This chapter contains an English translation of Alfred Tarski’s [1932] 2014e article Teorja długości okręgu w szkole średniej, which appeared in the October–December 1932 issue of the journal Parametr. The journal’s target audience consisted of gimnazjum teachers and their most serious students. For further information about that publication, consult section 9.7 of the present book.

Article

The math book. From Pythagoras to the 57th dimension. 250 milestones in the history of mathematics....

Clifford A Pickover

Chapter

The Unfortunates: Hypertext, Linearity and the Act of Reading

January 2007

Kaye Mitchell

On 20 February 1969, Panther Books (in association with Secker and Warburg) published B. S. Johnson’s new novel, The Unfortunates. This ‘book in a box’, as it would become known, featured twenty-seven individually bound and paginated chapters collected in a box, with only the first and last chapters identified as such; the intervening sections could thus be rearranged by the reader and read in ... [Show full abstract] any order they chose. Such formal experimentation was not unique—as several writers on Johnson, including Jonathan Coe, have acknowledged, the author was almost certainly aware of Marc Saporta’s entirely loose-leaved novel, Composition No. 1 (translated from French into English in 1963)—nevertheless, the format of The Unfortunates has afforded it no little notoriety, acclaim and commentary over the years.

Book

Full-text available

Mathematics Pocket Dictionary for Beginners (Symbols, Definitions, and Terms: An Introduction)

January 2022

This book is divided into two major sections: mathematical terms in English and mathematical symbols. This book provides alphabetical data regarding mathematical terms defined and translated into Indonesian in the first part. Furthermore, this book describes some symbols often used in learning mathematics in the second part. Furthermore, this book is suitable for reading by high school students, ... [Show full abstract] students, and lecturers who want to know several English terms in learning mathematics. In addition, it is hoped that this book can inspire readers to use English words in learning mathematics. For information, English terms in learning mathematics have specific characteristics compared to English terms in general.

Chapter

Information in Language

January 1984

M. J. Usher

We have already seen from chapter 1 that the idea of probability is absolutely basic in Information Theory. It is necessary to develop some of the important rules and results of probability theory before we can attempt to analyse the information content of a language such as English. In the mathematical sections of this book a fairly intuitive approach will be adopted, based on an understanding ... [Show full abstract] of the processes involved, rather than a strictly rigorous mathematical presentation. Mathematics will be viewed as a tool for the efficient representation and analysis of ideas, rather than a study for its own sake. We will avoid formal proofs except where such proofs are instructive or add to our understanding of the subject.