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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1039700698

Digital Object Identifier
doi:10.1305/ndjfl/1039700698

Mathematical Reviews number (MathSciNet)
MR1479370

Zentralblatt MATH identifier
0889.03052

Subjects
Primary: 03C62: Models of arithmetic and set theory [See also 03Hxx]
Secondary: 03C57: Effective and recursion-theoretic model theory [See also 03D45] 03D35: Undecidability and degrees of sets of sentences 03F30: First-order arithmetic and fragments

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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