Descriptive Set Theory And Forcing

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Classical Descriptive Set Theory

Author : Alexander Kechris
Publisher : Springer Science & Business Media
ISBN 13 : 1461241901
Total Pages : 419 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Classical Descriptive Set Theory by : Alexander Kechris

Download or read book Classical Descriptive Set Theory written by Alexander Kechris and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.

Descriptive Set Theory

Author : Yiannis N. Moschovakis
Publisher : American Mathematical Society
ISBN 13 : 1470479877
Total Pages : 518 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Descriptive Set Theory by : Yiannis N. Moschovakis

Download or read book Descriptive Set Theory written by Yiannis N. Moschovakis and published by American Mathematical Society. This book was released on 2025-01-31 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analysts at the turn of the 20th century, most prominently Lebesgue, and, initially, was concerned primarily with establishing regularity properties of Borel and Lebesgue measurable functions, and analytic, coanalytic, and projective sets. Its rapid development came to a halt in the late 1930s, primarily because it bumped against problems which were independent of classical axiomatic set theory. The field became very active again in the 1960s, with the introduction of strong set-theoretic hypotheses and methods from logic (especially recursion theory), which revolutionized it. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern ?effective? theory and the consequences of strong (especially determinacy) hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results (established since the 1980s) relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics. The book includes all the necessary background from (advanced) set theory, logic and recursion theory.

Descriptive Set Theory and Forcing

Author : Arnold W. Miller
Publisher : Cambridge University Press
ISBN 13 : 1107168066
Total Pages : 135 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Descriptive Set Theory and Forcing by : Arnold W. Miller

Download or read book Descriptive Set Theory and Forcing written by Arnold W. Miller and published by Cambridge University Press. This book was released on 2017-05-18 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes develop the theory of descriptive sets, leading up to a new proof of Louveau's separation theorem for analytic sets. A first course in mathematical logic and set theory is assumed, making this book suitable for advanced students and researchers.

Set Theory

Author : Ralf Schindler
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.

Forcing For Mathematicians

Author : Nik Weaver
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.

Set Theory for the Working Mathematician

Author : Krzysztof Ciesielski
Publisher : Cambridge University Press
ISBN 13 : 9780521594653
Total Pages : 256 pages
Book Rating : 4.5/5 (946 download)

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Book Synopsis Set Theory for the Working Mathematician by : Krzysztof Ciesielski

Download or read book Set Theory for the Working Mathematician written by Krzysztof Ciesielski and published by Cambridge University Press. This book was released on 1997-08-28 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents those methods of modern set theory most applicable to other areas of pure mathematics.

Descriptive Set Theory and Forcing

Author : Arnold W. Miller
Publisher : Cambridge University Press
ISBN 13 : 1316739317
Total Pages : 136 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis Descriptive Set Theory and Forcing by : Arnold W. Miller

Download or read book Descriptive Set Theory and Forcing written by Arnold W. Miller and published by Cambridge University Press. This book was released on 2017-05-18 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourth publication in the Lecture Notes in Logic series, Miller develops the necessary features of the theory of descriptive sets in order to present a new proof of Louveau's separation theorem for analytic sets. While some background in mathematical logic and set theory is assumed, the material is based on a graduate course given by the author at the University of Wisconsin, Madison, and is thus accessible to students and researchers alike in these areas, as well as in mathematical analysis.

Descriptive Set Theory and Definable Forcing

Author : Jindřich Zapletal
Publisher : American Mathematical Soc.
ISBN 13 : 0821834509
Total Pages : 158 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Descriptive Set Theory and Definable Forcing by : Jindřich Zapletal

Download or read book Descriptive Set Theory and Definable Forcing written by Jindřich Zapletal and published by American Mathematical Soc.. This book was released on 2004 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on the relationship between definable forcing and descriptive set theory; the forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum.

Appalachian Set Theory

Author : James Cummings
Publisher : Cambridge University Press
ISBN 13 : 1139852140
Total Pages : 433 pages
Book Rating : 4.1/5 (398 download)

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Book Synopsis Appalachian Set Theory by : James Cummings

Download or read book Appalachian Set Theory written by James Cummings and published by Cambridge University Press. This book was released on 2012-11-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes its name from a popular series of intensive mathematics workshops hosted at institutions in Appalachia and surrounding areas. At these meetings, internationally prominent set theorists give one-day lectures that focus on important new directions, methods, tools and results so that non-experts can begin to master these and incorporate them into their own research. Each chapter in this volume was written by the workshop leaders in collaboration with select student participants, and together they represent most of the meetings from the period 2006–2012. Topics covered include forcing and large cardinals, descriptive set theory, and applications of set theoretic ideas in group theory and analysis, making this volume essential reading for a wide range of researchers and graduate students.

Geometric Set Theory

Author : Paul B. Larson
Publisher : American Mathematical Soc.
ISBN 13 : 1470454629
Total Pages : 345 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometric Set Theory by : Paul B. Larson

Download or read book Geometric Set Theory written by Paul B. Larson and published by American Mathematical Soc.. This book was released on 2020-07-16 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.

Surveys in Set Theory

Author : A. R. D. Mathias
Publisher : Cambridge University Press
ISBN 13 : 0521277337
Total Pages : 257 pages
Book Rating : 4.5/5 (212 download)

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Book Synopsis Surveys in Set Theory by : A. R. D. Mathias

Download or read book Surveys in Set Theory written by A. R. D. Mathias and published by Cambridge University Press. This book was released on 1983-10-13 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Higher Infinite

Author : Akihiro Kanamori
Publisher : Springer Science & Business Media
ISBN 13 : 3540888675
Total Pages : 555 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis The Higher Infinite by : Akihiro Kanamori

Download or read book The Higher Infinite written by Akihiro Kanamori and published by Springer Science & Business Media. This book was released on 2008-11-23 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.

Combinatorial Set Theory

Author : Lorenz J. Halbeisen
Publisher : Springer
ISBN 13 : 3319602314
Total Pages : 586 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Combinatorial Set Theory by : Lorenz J. Halbeisen

Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer. This book was released on 2017-12-20 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.

Set Theory of the Continuum

Author : Haim Judah
Publisher : Springer Science & Business Media
ISBN 13 : 1461397545
Total Pages : 417 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Set Theory of the Continuum by : Haim Judah

Download or read book Set Theory of the Continuum written by Haim Judah and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.

The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

Author : W. Hugh Woodin
Publisher : Walter de Gruyter
ISBN 13 : 3110804735
Total Pages : 944 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal by : W. Hugh Woodin

Download or read book The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal written by W. Hugh Woodin and published by Walter de Gruyter. This book was released on 2013-02-01 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

The Structure of Models of Peano Arithmetic

Author : Roman Kossak
Publisher : Oxford University Press
ISBN 13 : 0198568274
Total Pages : 326 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis The Structure of Models of Peano Arithmetic by : Roman Kossak

Download or read book The Structure of Models of Peano Arithmetic written by Roman Kossak and published by Oxford University Press. This book was released on 2006-06-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students, research logicians and mathematicians, this much-awaited text covers over 40 years of work on relative classification theory for nonstandard models of arithmetic. The book covers basic isomorphism invariants: families of type realized in a model, lattices of elementary substructures and automorphism groups.

Introduction to Modern Set Theory

Author : Judith Roitman
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.