A theory of sets with the negation of the axiom of infinity

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Mathematical Logic Quarterly 39 (1):338-352 (1993)
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Abstract

In this paper we introduce a theory of finite sets FST with a strong negation of the axiom of infinity asserting that every set is provably bijective with a natural number. We study in detail the role of the axioms of Power Set, Choice, Regularity in FST, pointing out the relative dependences or independences among them. FST is shown to be provably equivalent to a fragment of Alternative Set Theory. Furthermore, the introduction of FST is motivated in view of a non-standard development. MSC: 03E30, 03E35

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10.1002/malq.19930390138

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References found in this work

A course in mathematical logic.J. L. Bell - 1977 - New York: sole distributors for the U.S.A. and Canada American Elsevier Pub. Co.. Edited by Moshé Machover.
A Course in Mathematical Logic.J. L. Bell & M. Machover - 1978 - British Journal for the Philosophy of Science 29 (2):207-208.
Models of ZF-set theory.Ulrich Felgner - 1971 - New York,: Springer Verlag.

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