## Notre Dame Journal of Formal Logic

### A Note on Induction, Abstraction, and Dedekind-Finiteness

G. Aldo Antonelli

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 9 May 2012

http://projecteuclid.org/euclid.ndjfl/1336588249

Digital Object Identifier
doi:10.1215/00294527-1715680

Mathematical Reviews number (MathSciNet)
MR2925276

Zentralblatt MATH identifier
06054424

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

Keywords
arithmetic induction neologicism

#### Citation

Antonelli, G. Aldo. A Note on Induction, Abstraction, and Dedekind-Finiteness. Notre Dame Journal of Formal Logic 53 (2012), no. 2, 187--192. doi:10.1215/00294527-1715680. http://projecteuclid.org/euclid.ndjfl/1336588249.

#### References

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