Mathematical Logic Quarterly 39 (1):338-352 (1993)
AbstractIn 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
Added to PP
Historical graph of downloads
References found in this work
A Course in Mathematical Logic.J. L. Bell - 1977 - Sole Distributors for the U.S.A. And Canada American Elsevier Pub. Co..
Set Theory. An Introduction to Independence Proofs.James E. Baumgartner & Kenneth Kunen - 1986 - Journal of Symbolic Logic 51 (2):462.
A Course in Mathematical Logic.J. L. Bell & M. Machover - 1978 - British Journal for the Philosophy of Science 29 (2):207-208.
Set Theory: An Introduction to Independence Proofs.Kenneth Kunen - 1980 - North-Holland.
Citations of this work
On Interpretations of Arithmetic and Set Theory.Richard Kaye & Tin Lok Wong - 2007 - Notre Dame Journal of Formal Logic 48 (4):497-510.
Hilbert Arithmetic as a Pythagorean Arithmetic: Arithmetic as Transcendental.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (54):1-24.