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OverviewThis 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. Full Product DetailsAuthor: Paul B. Larson , Jindrich ZapletalPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.617kg ISBN: 9781470454623ISBN 10: 1470454629 Pages: 340 Publication Date: 30 September 2020 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction. Equivalence relations: The virtual realm. Turbulence. Nested sequences of models. Balanced extensions of the Solovay model: Balanced Suslin forcing. Simplicial complex forcings. Ultrafilter forcings. Other forcings. Preserving cardinalities. Uniformization. Locally countable structures. The Silver divide. The arity divide. Other combinatorics. Bibliography. Index.ReviewsAuthor InformationPaul B. Larson, Miami University, Oxford, OH Jindrich Zapletal, University of Florida, Gainesville, FL, and Czech Academy of Sciences, Prague, Czech Republic Tab Content 6Author Website:Countries AvailableAll regions |
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