Author : Jindřich Zapletal
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 47,4 MB
Release : 2004
Category : Mathematics
ISBN : 0821834509
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 : Cambridge University Press
Page : 136 pages
File Size : 45,53 MB
Release : 2017-05-18
Category : Mathematics
ISBN : 1316739317
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 W. Miller
Publisher :
Page : 130 pages
File Size : 35,36 MB
Release : 2002-01-01
Category : Borel sets
ISBN : 9781568811765
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 : Jindrich Zapletal
Publisher : Cambridge University Press
Page : 7 pages
File Size : 39,60 MB
Release : 2008-02-07
Category : Mathematics
ISBN : 113946826X
Descriptive set theory and definable proper forcing are two areas of set theory that developed quite independently of each other. This monograph unites them and explores the connections between them. Forcing is presented in terms of quotient algebras of various natural sigma-ideals on Polish spaces, and forcing properties in terms of Fubini-style properties or in terms of determined infinite games on Boolean algebras. Many examples of forcing notions appear, some newly isolated from measure theory, dynamical systems, and other fields. The descriptive set theoretic analysis of operations on forcings opens the door to applications of the theory: absoluteness theorems for certain classical forcing extensions, duality theorems, and preservation theorems for the countable support iteration. Containing original research, this text highlights the connections that forcing makes with other areas of mathematics, and is essential reading for academic researchers and graduate students in set theory, abstract analysis and measure theory.
Author : Jindřich Zapletal
Publisher :
Page : 322 pages
File Size : 50,12 MB
Release : 2014-05-14
Category : Mathematics
ISBN : 9780511378942
Unites descriptive set theory and definable proper forcing and explores the relations between them. Both forcing and descriptive set theory are explained independently, their sub-areas described, following their commitment to each other. This text highlights the connections that forcing makes with other areas of mathematics, such as set theory, abstract analysis, and measure theory.--From publisher description.
Author : Arnold Miller
Publisher : Springer
Page : 144 pages
File Size : 26,7 MB
Release : 1995-09-18
Category : Mathematics
ISBN :
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 : Alexander Kechris
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 45,35 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461241901
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 : Nik Weaver
Publisher : World Scientific
Page : 153 pages
File Size : 30,71 MB
Release : 2014-01-24
Category : Mathematics
ISBN : 9814566020
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 : Y.N. Moschovakis
Publisher : Elsevier
Page : 651 pages
File Size : 45,33 MB
Release : 1987-01-01
Category : Science
ISBN : 0080963196
Now available in paperback, this monograph is a self-contained exposition of the main results and methods of descriptive set theory. It develops all the necessary background material from logic and recursion theory, and treats both classical descriptive set theory and the effective theory developed by logicians.
Author : Paul B. Larson
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 27,44 MB
Release : 2020-07-16
Category : Education
ISBN : 1470454629
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.
