Computability Forcing And Descriptive Set Theory
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Author |
: Jindřich Zapletal |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 158 |
Release |
: 2004 |
ISBN-10 |
: 9780821834503 |
ISBN-13 |
: 0821834509 |
Rating |
: 4/5 (03 Downloads) |
Synopsis Descriptive Set Theory and Definable Forcing by : Jindřich Zapletal
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.
Author |
: Arnold W. Miller |
Publisher |
: |
Total Pages |
: 130 |
Release |
: 2002-01-01 |
ISBN-10 |
: 1568811764 |
ISBN-13 |
: 9781568811765 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Descriptive Set Theory and Forcing by : Arnold W. Miller
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
Author |
: Arnold W. Miller |
Publisher |
: Cambridge University Press |
Total Pages |
: 136 |
Release |
: 2017-05-18 |
ISBN-10 |
: 9781316739310 |
ISBN-13 |
: 1316739317 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Descriptive Set Theory and Forcing by : Arnold W. Miller
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.
Author |
: Arnold Miller |
Publisher |
: Springer |
Total Pages |
: 144 |
Release |
: 1995-09-18 |
ISBN-10 |
: UOM:39015034997786 |
ISBN-13 |
: |
Rating |
: 4/5 (86 Downloads) |
Synopsis Descriptive Set Theory and Forcing by : Arnold Miller
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.
Author |
: Lucas Wansner |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 2023 |
ISBN-10 |
: OCLC:1378724532 |
ISBN-13 |
: |
Rating |
: 4/5 (32 Downloads) |
Synopsis Aspects of Forcing in Descriptive Set Theory and Computability Theory by : Lucas Wansner
Author |
: Alexander Kechris |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 419 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461241904 |
ISBN-13 |
: 1461241901 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Classical Descriptive Set Theory by : Alexander Kechris
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.
Author |
: Yiannis N. Moschovakis |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 521 |
Release |
: 2009-06-30 |
ISBN-10 |
: 9780821848135 |
ISBN-13 |
: 0821848135 |
Rating |
: 4/5 (35 Downloads) |
Synopsis Descriptive Set Theory by : Yiannis N. Moschovakis
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.
Author |
: Chi Tat Chong |
Publisher |
: World Scientific |
Total Pages |
: 185 |
Release |
: 2015-07-30 |
ISBN-10 |
: 9789814699969 |
ISBN-13 |
: 9814699969 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Forcing, Iterated Ultrapowers, And Turing Degrees by : Chi Tat Chong
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.
Author |
: Nik Weaver |
Publisher |
: World Scientific |
Total Pages |
: 153 |
Release |
: 2014-01-24 |
ISBN-10 |
: 9789814566025 |
ISBN-13 |
: 9814566020 |
Rating |
: 4/5 (25 Downloads) |
Synopsis Forcing For Mathematicians by : Nik Weaver
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.
Author |
: Sy-david Friedman |
Publisher |
: World Scientific |
Total Pages |
: 280 |
Release |
: 2017-06-22 |
ISBN-10 |
: 9789813223530 |
ISBN-13 |
: 9813223537 |
Rating |
: 4/5 (30 Downloads) |
Synopsis Sets And Computations by : Sy-david Friedman
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.