Geometric Set Theory - Couverture souple

Larson, Paul B.; Zapletal, Jindrich

Couverture souple

ISBN 10 : 1470454629 ISBN 13 : 9781470454623

Editeur : American Mathematical Society, 2020

Synopsis

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.

A propos du livre

À propos de l'auteur

Paul B. Larson, Miami University, Oxford, OH

Jindrich Zapletal, University of Florida, Gainesville, FL, and Czech Academy of Sciences, Prague, Czech Republic

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2020
• Langue: anglais
• ISBN 10: 1470454629
• ISBN 13: 9781470454623
• Reliure: Broché
• Nombre de pages: 340
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible