Notre Dame Journal of Formal Logic

Toward the Limits of the Tennenbaum Phenomenon

Paola D'Aquino


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.

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

First available in Project Euclid: 12 December 2002

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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


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.

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