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2012 A Note on Induction, Abstraction, and Dedekind-Finiteness
G. Aldo Antonelli
Notre Dame J. Formal Logic 53(2): 187-192 (2012). DOI: 10.1215/00294527-1715680

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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G. Aldo Antonelli. "A Note on Induction, Abstraction, and Dedekind-Finiteness." Notre Dame J. Formal Logic 53 (2) 187 - 192, 2012. https://doi.org/10.1215/00294527-1715680

Information

Published: 2012
First available in Project Euclid: 9 May 2012

zbMATH: 1256.03063
MathSciNet: MR2925276
Digital Object Identifier: 10.1215/00294527-1715680

Subjects:
Primary: 03A99

Keywords: arithmetic , induction , neologicism

Rights: Copyright © 2012 University of Notre Dame

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