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2007 Finiteness Axioms on Fragments of Intuitionistic Set Theory
Riccardo Camerlo
Notre Dame J. Formal Logic 48(4): 473-488 (2007). DOI: 10.1305/ndjfl/1193667705


It is proved that in a suitable intuitionistic, locally classical, version of the theory ZFC deprived of the axiom of infinity, the requirement that every set be finite is equivalent to the assertion that every ordinal is a natural number. Moreover, the theory obtained with the addition of these finiteness assumptions is equivalent to a theory of hereditarily finite sets, developed by Previale in "Induction and foundation in the theory of hereditarily finite sets." This solves some problems stated there. The analysis is undertaken using for each of these results a limited fragment of the relevant theory.


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Riccardo Camerlo. "Finiteness Axioms on Fragments of Intuitionistic Set Theory." Notre Dame J. Formal Logic 48 (4) 473 - 488, 2007.


Published: 2007
First available in Project Euclid: 29 October 2007

zbMATH: 1146.03039
MathSciNet: MR2357522
Digital Object Identifier: 10.1305/ndjfl/1193667705

Primary: 03E70 , 03F55

Keywords: finiteness axioms , induction axiom schema , intuitionistic set theories

Rights: Copyright © 2007 University of Notre Dame


Vol.48 • No. 4 • 2007
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