Axiomatic Set Theory
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Axiomatic Set Theory
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Author : Patrick Suppes
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04
Axiomatic Set Theory written by Patrick Suppes and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
Axiomatic Set Theory
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Author : Lev D. Beklemishev
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Axiomatic Set Theory written by Lev D. Beklemishev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Computers categories.
Axiomatic Set Theory
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.
Introduction To Axiomatic Set Theory
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Author : G. Takeuti
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Axiomatic Set Theory written by G. Takeuti 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 Mathematics categories.
In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH. Notes taken in 1963 by the second author were taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are high lighted, and second, the student who wishes to master the subject is com pelled to develop the detail on his own. However, an instructor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text.
One Hundred Years Of Axiomatic Set Theory
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Author :
language : fr
Publisher: Academia
Release Date : 2012-06-01
One Hundred Years Of Axiomatic Set Theory written by and has been published by Academia this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-01 with Social Science categories.
This Cahier du centre de logique is made of papers presented at the homonymous conference that was organized by the editors in October 2008 to celebrate the 100th birthday of axiomatic set theory. It can virtually be divided into two bundles of papers : one discussing systems related to Zermelo's, the other dealing more specifically with systems related to type theory and stratification, both of which treating of key notions in the axiomatization of set theory.
Intuitive Axiomatic Set Theory
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Author : José L Garciá
language : en
Publisher: CRC Press
Release Date : 2024-04-04
Intuitive Axiomatic Set Theory written by José L Garciá and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-04 with Mathematics categories.
Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable. The book has two parts. The first one presents, from the sole intuition of "collection" and "object", the axiomatic ZFC-theory. Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes. The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic. The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.
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).
Axiomatic Set Theory
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Author : R. Chuaqui
language : en
Publisher: Elsevier
Release Date : 1981
Axiomatic Set Theory written by R. Chuaqui and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Discovering Modern Set Theory I The Basics
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Author : Winfried Just
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Discovering Modern Set Theory I The Basics written by Winfried Just 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 1996 with Mathematics categories.
This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.
Set Theory An Introduction To Independence Proofs
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Author : K. Kunen
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Set Theory An Introduction To Independence Proofs written by K. Kunen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.