Notes on Logic and Set Theory

Author: P. T. Johnstone

Publisher: Cambridge University Press

ISBN: 9780521336925

Category: Mathematics

Page: 110

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A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.
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Handbook of Analysis and Its Foundations

Author: Eric Schechter

Publisher: Academic Press

ISBN: 9780080532998

Category: Mathematics

Page: 883

View: 9950

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Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
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Set Theory, Logic and Their Limitations

Author: Moshe Machover,Maurice Machover

Publisher: Cambridge University Press

ISBN: 9780521479981

Category: Mathematics

Page: 288

View: 5698

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This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gdel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
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Algebraic Set Theory

Author: Andri Joyal,Izak Moerdijk,Ieke Moerdijk

Publisher: Cambridge University Press

ISBN: 9780521558303

Category: Mathematics

Page: 123

View: 4061

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This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.
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Set Theory

A First Course

Author: Daniel W. Cunningham

Publisher: Cambridge University Press

ISBN: 1107120322

Category: Mathematics

Page: 262

View: 7250

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Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.
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Surveys in Set Theory

Author: A. R. D. Mathias

Publisher: Cambridge University Press

ISBN: 0521277337

Category: Mathematics

Page: 247

View: 4541

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This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Gödel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.
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Set Theory

Author: Andras Hajnal,Peter Hamburger

Publisher: Cambridge University Press

ISBN: 9780521596671

Category: Mathematics

Page: 316

View: 8664

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This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.
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A Course on Borel Sets

Author: S.M. Srivastava

Publisher: Springer Science & Business Media

ISBN: 9780387984124

Category: Mathematics

Page: 264

View: 6807

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A thorough introduction to Borel sets and measurable selections, acting as a stepping stone to descriptive set theory by presenting such important techniques as universal sets, prewellordering, scales, etc. It contains significant applications to other branches of mathematics and serves as a self-contained reference accessible by mathematicians in many different disciplines. Written in an easily understandable style, and using only naive set theory, general topology, analysis, and algebra, it is thus well suited for graduates exploring areas of mathematics for their research and for those requiring Borel sets and measurable selections in their work.
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