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ω-models of finite set theory
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Set Theory, Arithmetic, and Foundations of Mathematics
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Finite set theory, here denoted ZF fin , is the theory obtained by replacing the axiom of infinity by its negation in the usual axiomatization of ZF (Zermelo-Fraenkel set theory). An ω-model of ZF fin is a model in which every set has at most finitely many elements (as viewed externally). Mancini and Zambella (2001) employed the Bernays-Rieger method of permutations to construct a recursive ω-model of ZF fin that is nonstandard (i.e., not isomorphic to the hereditarily finite sets V ω ). In

doi:10.1017/cbo9780511910616.004
fatcat:gc42okd7s5dwtgbf7adkdkfmrq