Geometric set theory
by Larson, Paul B., (Paul Bradley)
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 …
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- Full title :Geometric set theory / Paul B. Larson, Jindřich Zapletal.
Summary
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.
Read More ↓Edition Statements
- Publication Date:©2020
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, Rhode Island
- Language:eng
- Publication Date:©2020
The Physical Object
- Description:ix, 330 pages : : illustrations ; : 26 cm.
Edition Identifiers
- ISBN:9781470454623, 1470454629
- oclc:on1157634566
- LC Classification:QA248
- Dewey Decimal:511.3/22
Table of 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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