ENGLISH

Geometric Set Theory

By Jindrich Zapletal , Paul B. Larson

Book information

Publisher
American Mathematical Society
Year
2020
ISBN
1470454629, 9781470454623
Language
english
Format
PDF
Filesize
4 MB (4096188 bytes)
Series
Mathematical Surveys and Monographs 248
Pages
340\344
Orientation
portrait
Paginated
yes
Scanned
no
Time added
2020-11-23 13:49:23

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. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.

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