Discovering Modern Set Theory 2
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Author |
: Winfried Just |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 230 |
Release |
: 1996 |
ISBN-10 |
: 9780821802663 |
ISBN-13 |
: 0821802666 |
Rating |
: 4/5 (63 Downloads) |
Synopsis Discovering Modern Set Theory. I: The Basics by : Winfried Just
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.
Author |
: Winfried Just and Martin Weese |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 244 |
Release |
: |
ISBN-10 |
: 0821872087 |
ISBN-13 |
: 9780821872086 |
Rating |
: 4/5 (87 Downloads) |
Synopsis Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician by : Winfried Just and Martin Weese
Author |
: Winfried Just |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 240 |
Release |
: 1996 |
ISBN-10 |
: 9780821805282 |
ISBN-13 |
: 0821805282 |
Rating |
: 4/5 (82 Downloads) |
Synopsis Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician by : Winfried Just
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.
Author |
: Judith Roitman |
Publisher |
: John Wiley & Sons |
Total Pages |
: 188 |
Release |
: 1990-01-16 |
ISBN-10 |
: 0471635197 |
ISBN-13 |
: 9780471635192 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Introduction to Modern Set Theory by : Judith Roitman
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.
Author |
: Jose Ferreiros |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 472 |
Release |
: 2001-11-01 |
ISBN-10 |
: 3764357495 |
ISBN-13 |
: 9783764357498 |
Rating |
: 4/5 (95 Downloads) |
Synopsis Labyrinth of Thought by : Jose Ferreiros
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
Author |
: Charles C Pinter |
Publisher |
: Courier Corporation |
Total Pages |
: 259 |
Release |
: 2014-07-23 |
ISBN-10 |
: 9780486497082 |
ISBN-13 |
: 0486497089 |
Rating |
: 4/5 (82 Downloads) |
Synopsis A Book of Set Theory by : Charles C Pinter
"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"--
Author |
: Michael Potter |
Publisher |
: Clarendon Press |
Total Pages |
: 362 |
Release |
: 2004-01-15 |
ISBN-10 |
: 9780191556432 |
ISBN-13 |
: 0191556432 |
Rating |
: 4/5 (32 Downloads) |
Synopsis Set Theory and its Philosophy by : Michael Potter
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Author |
: Alfred North Whitehead |
Publisher |
: |
Total Pages |
: 688 |
Release |
: 1910 |
ISBN-10 |
: UOM:39015002922881 |
ISBN-13 |
: |
Rating |
: 4/5 (81 Downloads) |
Synopsis Principia Mathematica by : Alfred North Whitehead
Author |
: Nikolai Konstantinovich Vereshchagin |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 130 |
Release |
: 2002 |
ISBN-10 |
: 9780821827314 |
ISBN-13 |
: 0821827316 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Basic Set Theory by : Nikolai Konstantinovich Vereshchagin
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.
Author |
: Robert Gardner Bartle |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 474 |
Release |
: 2001 |
ISBN-10 |
: 9780821808450 |
ISBN-13 |
: 0821808451 |
Rating |
: 4/5 (50 Downloads) |
Synopsis A Modern Theory of Integration by : Robert Gardner Bartle
This book is an introduction to a theory of the integral that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration.