### 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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Primary Subjects: 03A99
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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

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Digital Object Identifier: doi:10.1093/philmat/nkq010
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Mathematical Reviews (MathSciNet): MR2667904
Zentralblatt MATH: 1205.03055
Digital Object Identifier: doi:10.1215/00294527-2010-010
Project Euclid: euclid.ndjfl/1276284780
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Zentralblatt MATH: 1068.03051
Digital Object Identifier: doi:10.2178/bsl/1082986260
Project Euclid: euclid.bsl/1082986260