Abstract
AbstractLet V be the cumulative set theoretic hierarchy, generated from the empty set by taking powers at successor stages and unions at limit stages and. following [2], let the primitive language of set theory be the first order language which contains binary symbols for equality and membership only. Despite the existence of ∀∀-formulae in the primitive language, with two free variables, which are satisfiable in ∀ but not by finite sets ([5]). and therefore of ∃∃∀∀ sentences of the same language, which are undecidable in ZFC without the Axiom of Infinity, truth in V for ∃*∀∀-sentences of the primitive language, is decidable ([1]). Completeness of ZF with respect to such sentences follows.
Publisher
Cambridge University Press (CUP)
Reference7 articles.
1. Note on: The logically simplest form of the infinity axiom;Parlamento;Proceedings of the American Mathematical Society,1990
2. Bellè D. , The decision problem for extensional set theories, Ph.D. thesis , Universitàdi Siena, 1998.
3. The ∀n∃-Completeness of Zermelo-Fraenkel Set Theory
4. Decidability of ∀*∀-Sentences in Membership Theories
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