Geometric Set Theory
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Author
Publication
2020 - American Mathematical Society
Language
English
Word Count
85,000 words, Guess
Page Count
340 pages
Identifiers
- ISBN-139781470454623
- ISBN-101470454629
- Library of Congress Control Number2020009795
- OCLC Control Number1157634566
- Better World Books9781470454623
and 1 more
- Open LibraryOL29956640M
Classifications
- LCCQA248.L265 2020
- LCCQA248 .L265 2020
Description
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.
Subjects
Topics
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