## Tsukuba Journal of Mathematics

### Models of Peano arithmetic as modules over initial segments

#### Abstract

Let $M$ be a countable non-standard model of first order Peano arithmetic (PA) and $I$ a weakly definable proper initial segment that is closed under addition, multiplication and factorial. We show that there is another model $N$ of PA such that the structure of $I$-module of $M$ coincides with that of $N$ and the multiplication of $M$ coincides with that of $N$ on $I$ but does not coincide at some $(a, b)\not\in I^{2}$.

#### Article information

Source
Tsukuba J. Math., Volume 29, Number 1 (2005), 19-27.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496164891

Digital Object Identifier
doi:10.21099/tkbjm/1496164891

Mathematical Reviews number (MathSciNet)
MR2162828

Zentralblatt MATH identifier
1088.03035

#### Citation

Suzuki, Nobuya. Models of Peano arithmetic as modules over initial segments. Tsukuba J. Math. 29 (2005), no. 1, 19--27. doi:10.21099/tkbjm/1496164891. https://projecteuclid.org/euclid.tkbjm/1496164891