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Geometric set theory / Paul B. Larson, Jindřich Zapletal.
Author
Larson, Paul B. (Paul Bradley), 1970-
[Browse]
Format
Book
Language
English
Published/Created
Providence, Rhode Island : American Mathematical Society, [2020]
©2020
Description
ix, 330 pages : illustrations ; 26 cm.
Availability
Available Online
Mathematical Surveys and Monographs -2020
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA248 .L265 2020
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Details
Subject(s)
Descriptive set theory
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Equivalence relations (Set theory)
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Borel sets
[Browse]
Independence (Mathematics)
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Axiomatic set theory
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Forcing (Model theory)
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Author
Zapletal, Jindřich, 1969-
[Browse]
Series
Mathematical surveys and monographs ; no. 248.
[More in this series]
Mathematical surveys and monographs, 0076-5376 ; volume 248
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Summary note
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.
Bibliographic references
Includes bibliographical references and index.
Contents
The virtual realm
Turbulence
Nested sequences of models
Balanced Suslin forcing
Simplicial complex forcings
Ultrafilter forcings
Other forcings
Preserving cardinalities
Uniformization
Locally countable structures
The Silver divide
The arity divide
Other combinatorics.
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ISBN
9781470454623 (paperback)
1470454629 (paperback)
LCCN
2020009795
OCLC
1157634566
Statement on language in description
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
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Geometric set theory / Paul B. Larson & Jindřich Zapletal.
id
99129035459306421