Computability Forcing And Descriptive Set Theory

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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.

Descriptive Set Theory and Forcing

Author : Arnold W. Miller
Publisher :
ISBN 13 : 9781568811765
Total Pages : 130 pages
Book Rating : 4.8/5 (117 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 . This book was released on 2002-01-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is based on a graduate course given by the author at the University of Wisconsin. It presents an exposition of basic material from descriptive set theory (the general theory of Borel sets and projective sets), leading up to a new proof of Louveau's separation theorem for analytic sets. It assumes some background in mathematical logic and set theory, and should be of interest to reseachers and advanced students in these areas as well as in mathematical analysis. 4

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 Forcing

Author : Arnold Miller
Publisher : Springer
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Descriptive Set Theory and Forcing by : Arnold Miller

Download or read book Descriptive Set Theory and Forcing written by Arnold Miller and published by Springer. This book was released on 1995-09-18 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate course assumes some knowledge of forcing as well as some elementary mathematical logic, e.g. the Lowenheim-Skolem Theorem. The first half deals with the general area of Borel hierarchies, probing lines of enquiry such as the possible lengths of a Borel hierarchy in a separable metric space. The second half goes on to include Harrington's Theorem together with a proof and applications of Louveau's Theorem on hyperprojective parameters.

Aspects of Forcing in Descriptive Set Theory and Computability Theory

Author : Lucas Wansner
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Aspects of Forcing in Descriptive Set Theory and Computability Theory by : Lucas Wansner

Download or read book Aspects of Forcing in Descriptive Set Theory and Computability Theory written by Lucas Wansner and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Soc.
ISBN 13 : 0821848135
Total Pages : 521 pages
Book Rating : 4.8/5 (218 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 Soc.. This book was released on 2009-06-30 with total page 521 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.

Forcing, Iterated Ultrapowers, And Turing Degrees

Author : Chi Tat Chong
Publisher : World Scientific
ISBN 13 : 9814699969
Total Pages : 185 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Forcing, Iterated Ultrapowers, And Turing Degrees by : Chi Tat Chong

Download or read book Forcing, Iterated Ultrapowers, And Turing Degrees written by Chi Tat Chong and published by World Scientific. This book was released on 2015-07-30 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2010 and 2011 Asian Initiative for Infinity Logic Summer Schools. The major topics covered set theory and recursion theory, with particular emphasis on forcing, inner model theory and Turing degrees, offering a wide overview of ideas and techniques introduced in contemporary research in the field of mathematical logic.

Sets And Computations

Author : Sy-david Friedman
Publisher : World Scientific
ISBN 13 : 9813223537
Total Pages : 280 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Sets And Computations by : Sy-david Friedman

Download or read book Sets And Computations written by Sy-david Friedman and published by World Scientific. This book was released on 2017-06-22 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents in this volume are based on the program Sets and Computations that was held at the Institute for Mathematical Sciences, National University of Singapore from 30 March until 30 April 2015. This special collection reports on important and recent interactions between the fields of Set Theory and Computation Theory. This includes the new research areas of computational complexity in set theory, randomness beyond the hyperarithmetic, powerful extensions of Goodstein's theorem and the capturing of large fragments of set theory via elementary-recursive structures.Further chapters are concerned with central topics within Set Theory, including cardinal characteristics, Fraïssé limits, the set-generic multiverse and the study of ideals. Also Computation Theory, which includes computable group theory and measure-theoretic aspects of Hilbert's Tenth Problem. A volume of this broad scope will appeal to a wide spectrum of researchers in mathematical logic.

Algebraic Computability and Enumeration Models

Author : Cyrus F. Nourani
Publisher : CRC Press
ISBN 13 : 1771882484
Total Pages : 304 pages
Book Rating : 4.7/5 (718 download)

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Book Synopsis Algebraic Computability and Enumeration Models by : Cyrus F. Nourani

Download or read book Algebraic Computability and Enumeration Models written by Cyrus F. Nourani and published by CRC Press. This book was released on 2016-02-24 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples

Structure And Randomness In Computability And Set Theory

Author : Douglas Cenzer
Publisher : World Scientific
ISBN 13 : 9813228245
Total Pages : 387 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Structure And Randomness In Computability And Set Theory by : Douglas Cenzer

Download or read book Structure And Randomness In Computability And Set Theory written by Douglas Cenzer and published by World Scientific. This book was released on 2020-10-02 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium.

Fine Structure and Class Forcing

Author : Sy D. Friedman
Publisher : Walter de Gruyter
ISBN 13 : 9783110167771
Total Pages : 240 pages
Book Rating : 4.1/5 (677 download)

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Book Synopsis Fine Structure and Class Forcing by : Sy D. Friedman

Download or read book Fine Structure and Class Forcing written by Sy D. Friedman and published by Walter de Gruyter. This book was released on 2000 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Fine Structure and Class Forcing".

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.

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.

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.

Set Theory

Author : George A. Duckett
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781533549976
Total Pages : 208 pages
Book Rating : 4.5/5 (499 download)

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Book Synopsis Set Theory by : George A. Duckett

Download or read book Set Theory written by George A. Duckett and published by Createspace Independent Publishing Platform. This book was released on 2016-06-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you have a question about Set Theory this is the book with the answers. Set Theory: Questions and Answers takes some of the best questions and answers asked on the mathoverflow.stackexchange.com website. You can use this book to look up commonly asked questions, browse questions on a particular topic, compare answers to common topics, check out the original source and much more. This book has been designed to be very easy to use, with many internal references set up that makes browsing in many different ways possible. Topics covered include: Logic, Forcing, Large Cardinals, Axiom of Choice, Set Theory, Reference Request, Measure Theory, General Topology, Descriptive Set Theory, Model Theory, Category Theory, Real Analysis, Order Theory, Computability Theory, Math Philosophy, Combinatorics, Ultrafilters, Ordinal Numbers, Continuum Hypothesis and many more."

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.