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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…
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Editions
1 edition- Other · English · 2020American Mathematical Society · 340 pages · 9781470454623
MathematicsDescriptive set theoryEquivalence relations (Set theory)Borel setsIndependence (Mathematics)Axiomatic set theoryForcing (Model theory)