Models And Proofs Of Independence In Axiomatic Set Theory
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Models And Proofs Of Independence In Axiomatic Set Theory
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Author : Elliot Mendelson
language : en
Publisher:
Release Date : 1952
Models And Proofs Of Independence In Axiomatic Set Theory written by Elliot Mendelson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Axioms categories.
Sets Models And Proofs
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Author : Ieke Moerdijk
language : en
Publisher: Springer
Release Date : 2018-11-23
Sets Models And Proofs written by Ieke Moerdijk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-23 with Mathematics categories.
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.
Set Theory
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Author : Ralf Schindler
language : en
Publisher: Springer
Release Date : 2014-05-22
Set Theory written by Ralf Schindler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-22 with Mathematics categories.
This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing and descriptive set theory. The following topics are covered: • Forcing and constructability • The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal • Fine structure theory and a modern approach to sharps • Jensen’s Covering Lemma • The equivalence of analytic determinacy with sharps • The theory of extenders and iteration trees • A proof of projective determinacy from Woodin cardinals. Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.
Philosophy Of Mathematics
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Author : Stewart Shapiro
language : en
Publisher: Oxford University Press
Release Date : 1997-08-07
Philosophy Of Mathematics written by Stewart Shapiro and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-07 with Philosophy categories.
Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
Axiomatic Set Theory Part 1
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Author : Dana S. Scott
language : en
Publisher: American Mathematical Soc.
Release Date : 1971-12-31
Axiomatic Set Theory Part 1 written by Dana S. Scott and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-12-31 with Mathematics categories.
Simplified Independence Proofs
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Author :
language : en
Publisher: Academic Press
Release Date : 2011-08-29
Simplified Independence Proofs written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-29 with Mathematics categories.
Simplified Independence Proofs
An Introduction To Independence For Analysts
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Author : H. G. Dales
language : en
Publisher: Cambridge University Press
Release Date : 1987-12-10
An Introduction To Independence For Analysts written by H. G. Dales and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-12-10 with Mathematics categories.
Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH.
Introduction To Axiomatic Set Theory
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Author : J.L. Krivine
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Axiomatic Set Theory written by J.L. Krivine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
This book presents the classic relative consistency proofs in set theory that are obtained by the device of 'inner models'. Three examples of such models are investigated in Chapters VI, VII, and VIII; the most important of these, the class of constructible sets, leads to G6del's result that the axiom of choice and the continuum hypothesis are consistent with the rest of set theory [1]I. The text thus constitutes an introduction to the results of P. Cohen concerning the independence of these axioms [2], and to many other relative consistency proofs obtained later by Cohen's methods. Chapters I and II introduce the axioms of set theory, and develop such parts of the theory as are indispensable for every relative consistency proof; the method of recursive definition on the ordinals being an import ant case in point. Although, more or less deliberately, no proofs have been omitted, the development here will be found to require of the reader a certain facility in naive set theory and in the axiomatic method, such e as should be achieved, for example, in first year graduate work (2 cycle de mathernatiques).
The Axiom Of Choice
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Author : Thomas J. Jech
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
The Axiom Of Choice written by Thomas J. Jech and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
A Book Of Set Theory
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Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2014-06-01
A Book Of Set Theory written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-01 with Mathematics categories.
Accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Topics include classes and sets, functions, natural and cardinal numbers, arithmetic of ordinal numbers, and more. 1971 edition with new material by author.