The Axiom of Choice

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Publisher : Courier Corporation
ISBN 13 : 0486466248
Total Pages : 226 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis The Axiom of Choice by : Thomas J. Jech

Download or read book The Axiom of Choice written by Thomas J. Jech and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Forcing For Mathematicians

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Publisher : World Scientific
ISBN 13 : 9814566020
Total Pages : 153 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Forcing For Mathematicians by : Nik Weaver

Download or read book Forcing For Mathematicians written by Nik Weaver and published by World Scientific. This book was released on 2014-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics.

Notes on Set Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1475741537
Total Pages : 280 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Notes on Set Theory by : Yiannis Moschovakis

Download or read book Notes on Set Theory written by Yiannis Moschovakis and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.

Nonstandard Models of Arithmetic and Set Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 0821835351
Total Pages : 184 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Nonstandard Models of Arithmetic and Set Theory by : Ali Enayat

Download or read book Nonstandard Models of Arithmetic and Set Theory written by Ali Enayat and published by American Mathematical Soc.. This book was released on 2004 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of non-standardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and non-Euclidean geometries. Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory.

The Axiom of Constructibility

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Publisher : Springer
ISBN 13 : 354037034X
Total Pages : 105 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Axiom of Constructibility by : K. J. Devlin

Download or read book The Axiom of Constructibility written by K. J. Devlin and published by Springer. This book was released on 2006-11-15 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Discovering Modern Set Theory. I: The Basics

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Publisher : American Mathematical Soc.
ISBN 13 : 0821802666
Total Pages : 230 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Discovering Modern Set Theory. I: The Basics by : Winfried Just

Download or read book Discovering Modern Set Theory. I: The Basics written by Winfried Just and published by American Mathematical Soc.. This book was released on 1996 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Philosophy of Set Theory

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Publisher : Courier Corporation
ISBN 13 : 0486138550
Total Pages : 258 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Philosophy of Set Theory by : Mary Tiles

Download or read book The Philosophy of Set Theory written by Mary Tiles and published by Courier Corporation. This book was released on 2012-03-08 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

Homotopy Type Theory: Univalent Foundations of Mathematics

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Author :
Publisher : Univalent Foundations
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4./5 ( download)

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Book Synopsis Homotopy Type Theory: Univalent Foundations of Mathematics by :

Download or read book Homotopy Type Theory: Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Model Theory

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Publisher :
ISBN 13 : 9780720422009
Total Pages : 0 pages
Book Rating : 4.4/5 (22 download)

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Book Synopsis Model Theory by :

Download or read book Model Theory written by and published by . This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Book of Set Theory

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Author :
Publisher : Courier Corporation
ISBN 13 : 0486497089
Total Pages : 259 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Book of Set Theory by : Charles C Pinter

Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Introduction to Modern Set Theory

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Publisher : John Wiley & Sons
ISBN 13 : 9780471635192
Total Pages : 188 pages
Book Rating : 4.6/5 (351 download)

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Book Synopsis Introduction to Modern Set Theory by : Judith Roitman

Download or read book Introduction to Modern Set Theory written by Judith Roitman and published by John Wiley & Sons. This book was released on 1990-01-16 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Sets for Mathematics

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Publisher : Cambridge University Press
ISBN 13 : 9780521010603
Total Pages : 280 pages
Book Rating : 4.0/5 (16 download)

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Book Synopsis Sets for Mathematics by : F. William Lawvere

Download or read book Sets for Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2003-01-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

Model Theory : An Introduction

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Publisher : Springer Science & Business Media
ISBN 13 : 0387227342
Total Pages : 342 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Model Theory : An Introduction by : David Marker

Download or read book Model Theory : An Introduction written by David Marker and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures

From Sets and Types to Topology and Analysis

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Publisher : Oxford University Press
ISBN 13 : 0198566514
Total Pages : 371 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis From Sets and Types to Topology and Analysis by : Laura Crosilla

Download or read book From Sets and Types to Topology and Analysis written by Laura Crosilla and published by Oxford University Press. This book was released on 2005-10-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the foundations and practice of constructive mathematics, this text focusses on the contrast between the theoretical developments - which have been most useful for computer science - and more specific efforts on constructive analysis, algebra and topology.

Set Theory

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Publisher : Springer
ISBN 13 : 3319067257
Total Pages : 335 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Set Theory by : Ralf Schindler

Download or read book Set Theory written by Ralf Schindler and published by Springer. This book was released on 2014-05-22 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Model Theory

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Author :
Publisher : Springer
ISBN 13 : 3540387579
Total Pages : 181 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Set Theory and Model Theory by : R.B. Jensen

Download or read book Set Theory and Model Theory written by R.B. Jensen and published by Springer. This book was released on 2006-12-08 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Set Theory and the Continuum Problem

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Publisher :
ISBN 13 : 9780486474847
Total Pages : 0 pages
Book Rating : 4.4/5 (748 download)

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Book Synopsis Set Theory and the Continuum Problem by : Raymond M. Smullyan

Download or read book Set Theory and the Continuum Problem written by Raymond M. Smullyan and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.