The Forcing Method In Set Theory

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The Forcing Method In Set Theory

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Author : Matteo Viale
language : en
Publisher: Springer Nature
Release Date : 2024-11-11

The Forcing Method In Set Theory written by Matteo Viale and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-11 with Mathematics categories.

The main aim of this book is to provide a compact self-contained presentation of the forcing technique devised by Cohen to establish the independence of the continuum hypothesis from the axioms of set theory. The book follows the approach to the forcing technique via Boolean valued semantics independently introduced by Vopenka and Scott/Solovay; it develops out of notes I prepared for several master courses on this and related topics and aims to provide an alternative (and more compact) account of this topic with respect to the available classical textbooks. The aim of the book is to take up a reader with familiarity with logic and set theory at the level of an undergraduate course on both topics (e.g., familiar with most of the content of introductory books on first-order logic and set theory) and bring her/him to page with the use of the forcing method to produce independence (or undecidability results) in mathematics. Familiarity of the reader with general topology would also be quite helpful; however, the book provides a compact account of all the needed results on this matter. Furthermore, the book is organized in such a way that many of its parts can also be read by scholars with almost no familiarity with first-order logic and/or set theory. The book presents the forcing method outlining, in many situations, the intersections of set theory and logic with other mathematical domains. My hope is that this book can be appreciated by scholars in set theory and by readers with a mindset oriented towards areas of mathematics other than logic and a keen interest in the foundations of mathematics.

Forcing For Mathematicians

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Author : Nik Weaver
language : en
Publisher: World Scientific
Release Date : 2014-01-24

Forcing For Mathematicians written by Nik Weaver and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-24 with Mathematics categories.

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.

The Forcing Method In Set Theory

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Author : Matteo Viale
language : en
Publisher:
Release Date : 2024

The Forcing Method In Set Theory written by Matteo Viale and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Logic, Symbolic and mathematical categories.

The main aim of this book is to provide a compact self-contained presentation of the forcing technique devised by Cohen to establish the independence of the continuum hypothesis from the axioms of set theory. The book follows the approach to the forcing technique via Boolean valued semantics independently introduced by Vopenka and Scott/Solovay; it develops out of notes I prepared for several master courses on this and related topics and aims to provide an alternative (and more compact) account of this topic with respect to the available classical textbooks. The aim of the book is to take up a reader with familiarity with logic and set theory at the level of an undergraduate course on both topics (e.g., familiar with most of the content of introductory books on first-order logic and set theory) and bring her/him to page with the use of the forcing method to produce independence (or undecidability results) in mathematics. Familiarity of the reader with general topology would also be quite helpful; however, the book provides a compact account of all the needed results on this matter. Furthermore, the book is organized in such a way that many of its parts can also be read by scholars with almost no familiarity with first-order logic and/or set theory. The book presents the forcing method outlining, in many situations, the intersections of set theory and logic with other mathematical domains. My hope is that this book can be appreciated by scholars in set theory and by readers with a mindset oriented towards areas of mathematics other than logic and a keen interest in the foundations of mathematics.

Combinatorial Set Theory

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Author : Lorenz J. Halbeisen
language : en
Publisher: Springer
Release Date : 2017-12-20

Combinatorial Set Theory written by Lorenz J. Halbeisen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-20 with Mathematics categories.

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.

Topics In Set Theory

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Author : Mohamed Bekkali
language : en
Publisher: Springer
Release Date : 2006-12-08

Topics In Set Theory written by Mohamed Bekkali and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

During the Fall Semester of 1987, Stevo Todorcevic gave a series of lectures at the University of Colorado. These notes of the course, taken by the author, give a novel and fast exposition of four chapters of Set Theory. The first two chapters are about the connection between large cardinals and Lebesque measure. The third is on forcing axioms such as Martin's axiom or the Proper Forcing Axiom. The fourth chapter looks at the method of minimal walks and p-functions and their applications. The book is addressed to researchers and graduate students interested in Set Theory, Set-Theoretic Topology and Measure Theory.

Set Theory And The Continuum Hypothesis

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Author : Paul J. Cohen
language : en
Publisher: Courier Corporation
Release Date : 2008-12-09

Set Theory And The Continuum Hypothesis written by Paul J. Cohen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-09 with Mathematics categories.

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Set Theory For The Working Mathematician

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Author : Krzysztof Ciesielski
language : en
Publisher: Cambridge University Press
Release Date : 1997-08-28

Set Theory For The Working Mathematician written by Krzysztof Ciesielski 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 1997-08-28 with Mathematics categories.

Presents those methods of modern set theory most applicable to other areas of pure mathematics.

Axiomatic Set Theory

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Author : G. Takeuti
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Axiomatic Set Theory written by G. Takeuti 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 2013-12-01 with Mathematics categories.

This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained.

The Axiom Of Determinacy Forcing Axioms And The Nonstationary Ideal

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Author : W. Hugh Woodin
language : en
Publisher: Walter de Gruyter
Release Date : 2010

The Axiom Of Determinacy Forcing Axioms And The Nonstationary Ideal written by W. Hugh Woodin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This is the revised edition of a well-established monograph on the identification of a canonical model in which the Continuum Hypothesis is false. Written by an expert in the field, it is directed to researchers and advanced graduate students in Mat

The Axiom Of Choice

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Author : Thomas J. Jech
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01

The Axiom Of Choice written by Thomas J. Jech and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.

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.