Discovering Modern Set Theory The Basics
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Discovering Modern Set Theory The Basics
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Author : Winfried Just
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Discovering Modern Set Theory 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 is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.
Discovering Modern Set Theory Ii Set Theoretic Tools For Every Mathematician
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Author : Winfried Just
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Discovering Modern Set Theory Ii Set Theoretic Tools For Every Mathematician 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 Set theory categories.
This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. The second volume is intended as a bridge between introductory set theory courses such as the first volume and advanced monographs that cover selected branches of set theory. The authors give short but rigorous introductions to set-theoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle, and the use of elementary submodels. Great care is taken to motivate concepts and theorems presented.
Discovering Modern Set Theory
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Author : Winfried Just
language : en
Publisher:
Release Date : 1996
Discovering Modern Set Theory written by Winfried Just and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Set theory categories.
Discovering Modern Set Theory Ii Set Theoretic Tools For Every Mathematician
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Author : Winfried Just and Martin Weese
language : en
Publisher: American Mathematical Soc.
Release Date :
Discovering Modern Set Theory Ii Set Theoretic Tools For Every Mathematician written by Winfried Just and Martin Weese 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 with Set theory categories.
Introduction To Modern Set Theory
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Author : Judith Roitman
language : en
Publisher: John Wiley & Sons
Release Date : 1990-01-16
Introduction To Modern Set Theory written by Judith Roitman and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-16 with Mathematics categories.
This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.
Fundamentals Of Contemporary Set Theory
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Author : K. J. Devlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fundamentals Of Contemporary Set Theory written by K. J. Devlin 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.
This book is intended to provide an account of those parts of contemporary set theory which are of direct relevance to other areas of pure mathematics. The intended reader is either an advanced level undergraduate, or a beginning graduate student in mathematics, or else an accomplished mathematician who desires or needs a familiarity with modern set theory. The book is written in a fairly easy going style, with a minimum of formalism (a format characteristic of contemporary set theory) • In Chapter I the basic principles of set theory are developed in a "naive" tl manner. Here the notions of "set I II union " , "intersection", "power set" I "relation" I "function" etc. are defined and discussed. One assumption in writing this chapter has been that whereas the reader may have met all of these concepts before, and be familiar with their usage, he may not have considered the various notions as forming part of the continuous development of a pure subject (namely set theory) • Consequently, our development is at the same time rigorous and fast. Chapter II develops the theory of sets proper. Starting with the naive set theory of Chapter I, we begin by asking the question "What is a set?" Attempts to give a rLgorous answer lead naturally to the axioms of set theory introduced by Zermelo and Fraenkel, which is the system taken as basic in this book.
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.
Set Theory For The Working Mathematician
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Author : Krzysztof Ciesielski
language : en
Publisher: Cambridge University Press
Release Date : 1997-08-28
Set Theory For The Working Mathematician written by Krzysztof Ciesielski 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 1997-08-28 with Mathematics categories.
Presents those methods of modern set theory most applicable to other areas of pure mathematics.
Basic Set Theory
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Author : Nikolai Konstantinovich Vereshchagin
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Basic Set Theory written by Nikolai Konstantinovich Vereshchagin 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 2002 with Set theory categories.
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
The Joy Of Sets
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Author : Keith Devlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Joy Of Sets written by Keith Devlin 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.
This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.