Discovering Modern Set Theory
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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 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
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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.
Discovering Modern Set Theory 2
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Author : Winfried Just
language : en
Publisher:
Release Date : 1997
Discovering Modern Set Theory 2 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 1997 with categories.
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.
Fundamentals Of Contemporary Set Theory
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Author : Keith J. Devlin
language : en
Publisher: Springer Science & Business Media
Release Date : 1979
Fundamentals Of Contemporary Set Theory written by Keith 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 1979 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 : Andras Hajnal
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-11
Set Theory written by Andras Hajnal 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 1999-11-11 with Mathematics categories.
This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.
Introduction To Modern Set Theory
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Author : Judith Roitman
language : en
Publisher: Virginia Commonwealth University Mathematics
Release Date : 2011
Introduction To Modern Set Theory written by Judith Roitman and has been published by Virginia Commonwealth University Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Set theory categories.
This book is designed for a one-semester course in set theory at the advanced undergraduate or beginning graduate level. Three features are the full integration into the text of the study of models of set theory, the use of illustrative examples both in the text and in the exercises, and the integration of consistency results and large cardinals into the text early on. This book is aimed at two audiences: students who are interested in studying set theory for its own sake, and students in other areas who may be curious about applications of set theory to their field. In particular, great care is taken to develop the intuitions that lie behind modern, as well as classical, set theory, and to connect set theory with the rest of mathematics.
The Joy Of Sets
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Author : Keith J. Devlin
language : en
Publisher: Springer
Release Date : 1993-01-01
The Joy Of Sets written by Keith J. Devlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mengenlehre categories.
"This book provides an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Intended for advanced undergraduates and beginning graduate students, the text is written in an easy-going style, with a minimum of formalism. The book begins with a review of "naive" set theory; it then develops the Zermelo-Fraenkel axioms of the theory, showing how they arise naturally from a rigorous answer to the question, "what is a set?" After discussing the ordinal and cardinal numbers, the book then delves into contemporary set theory, covering such topics as: the Borel hierarchy, stationary sets and regressive functions, and Lebesgue measure. Two chapters present an extension of the Zermelo-Fraenkel theory, discussing the axiom of constructibility and the question of provability in set theory. A final chapter presents an account of an alternative conception of set theory that has proved useful in computer science, the non-well-founded set theory of Peter Aczel"--Back cover.