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2000 A Single Axiom for Set Theory
David Bennett
Notre Dame J. Formal Logic 41(2): 152-170 (2000). DOI: 10.1305/ndjfl/1038234609


Axioms in set theory typically have the form $\forall z \exists y\forall x(x \in y \leftrightarrow F x z )$, where $F$ is a relation which links $x$ with $z$ in some way. In this paper we introduce a particular linkage relation $L$ and a single axiom based on $L$ from which all the axioms of $\mathrm{Z}$ (Zermelo set theory) can be derived as theorems. The single axiom is presented both in informal and formal versions. This calls for some discussion of pertinent features of formal and informal axiomatic method and some discussion of pertinent features of the system $\mathrm{S}$ of set theory to be erected on the single axiom. $\mathrm{S}$ is shown to be somewhat stronger than $\mathrm{Z}$, but much weaker than $\mathrm{ZF}$ (Zermelo-Fraenkel set theory).


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David Bennett. "A Single Axiom for Set Theory." Notre Dame J. Formal Logic 41 (2) 152 - 170, 2000.


Published: 2000
First available in Project Euclid: 25 November 2002

zbMATH: 1015.03050
MathSciNet: MR1932227
Digital Object Identifier: 10.1305/ndjfl/1038234609

Primary: 03E30
Secondary: 00A30

Keywords: axiom , basic , Cantorian , descendant , foundation , links , set , single

Rights: Copyright © 2000 University of Notre Dame


Vol.41 • No. 2 • 2000
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