A Note on Induction, Abstraction, and Dedekind-Finiteness
G. Aldo Antonelli
Source: Notre Dame J. Formal Logic Volume 53, Number 2
(2012), 187-192.
Abstract
The purpose of this note is to present a simplification of the system of arithmetical axioms given in previous work; specifically, it is shown how the induction principle can in fact be obtained from the remaining axioms, without the need of explicit postulation. The argument might be of more general interest, beyond the specifics of the proposed axiomatization, as it highlights the interaction of the notion of Dedekind-finiteness and the induction principle.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1336588249
Digital Object Identifier: doi:10.1215/00294527-1715680
Mathematical Reviews number (MathSciNet): MR2925276
Zentralblatt MATH identifier: 06054424
References
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Mathematical Reviews (MathSciNet): MR2728752
Zentralblatt MATH: 1217.03004
Digital Object Identifier: doi:10.1093/philmat/nkq010
Antonelli, G. A., "Numerical abstraction via the Frege quantifier", Notre Dame Journal of Formal Logic, vol. 51 (2010), pp. 161–79.
Mathematical Reviews (MathSciNet): MR2667904
Zentralblatt MATH: 1205.03055
Digital Object Identifier: doi:10.1215/00294527-2010-010
Project Euclid: euclid.ndjfl/1276284780
Boolos, G., "For every ${A}$ there is a ${B}$", Linguistic Inquiry, vol. 12 (1981), pp. 465–66.
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Mathematical Reviews (MathSciNet): MR2062415
Zentralblatt MATH: 1068.03051
Digital Object Identifier: doi:10.2178/bsl/1082986260
Project Euclid: euclid.bsl/1082986260
Notre Dame Journal of Formal Logic
