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.

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Lewis Library - Stacks QA248 .L265 2020 Browse related items Request

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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.
    ISBN
    • 9781470454623 (paperback)
    • 1470454629 (paperback)
    LCCN
    2020009795
    OCLC
    1157634566
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