Notre Dame Journal of Formal Logic

A Note on Induction, Abstraction, and Dedekind-Finiteness

G. Aldo Antonelli

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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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Notre Dame J. Formal Logic Volume 53, Number 2 (2012), 187-192.

First available in Project Euclid: 9 May 2012

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Primary: 03A99: None of the above, but in this section

arithmetic induction neologicism


Antonelli, G. Aldo. A Note on Induction, Abstraction, and Dedekind-Finiteness. Notre Dame J. Formal Logic 53 (2012), no. 2, 187--192. doi:10.1215/00294527-1715680.

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