## Notre Dame Journal of Formal Logic

### Toward the Limits of the Tennenbaum Phenomenon

Paola D'Aquino

#### Abstract

We consider the theory ${\rm PA}^{＃}$ and its weak fragments in the language of arithmetic expanded with the functional symbol $＃$. We prove that ${\rm PA}^{＃}$ and its weak fragments, down to $\forall E_1^{＃}({\bf N})$ and $IE_1^{-＃}$, are subject to the Tennenbaum phenomenon with respect to $+$, $\cdot$, and $＃$. For the last two theories it is still unknown if they may have nonstandard recursive models in the usual language of arithmetic.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 38, Number 1 (1997), 81-92.

Dates
First available in Project Euclid: 12 December 2002

https://projecteuclid.org/euclid.ndjfl/1039700698

Digital Object Identifier
doi:10.1305/ndjfl/1039700698

Mathematical Reviews number (MathSciNet)
MR1479370

Zentralblatt MATH identifier
0889.03052

#### Citation

D'Aquino, Paola. Toward the Limits of the Tennenbaum Phenomenon. Notre Dame J. Formal Logic 38 (1997), no. 1, 81--92. doi:10.1305/ndjfl/1039700698. https://projecteuclid.org/euclid.ndjfl/1039700698

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