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.
Citation
Paola D'Aquino. "Toward the Limits of the Tennenbaum Phenomenon." Notre Dame J. Formal Logic 38 (1) 81 - 92, Winter 1997. https://doi.org/10.1305/ndjfl/1039700698
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