Toward the Limits of the Tennenbaum Phenomenon

Notre Dame Journal of Formal Logic 38 (1):81-92 (1997)
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Abstract

We consider the theory and its weak fragments in the language of arithmetic expanded with the functional symbol . We prove that and its weak fragments, down to and , are subject to the Tennenbaum phenomenon with respect to , , 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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10.1305/ndjfl/1039700698

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Citations of this work

Computational Structuralism &dagger.Volker Halbach & Leon Horsten - 2005 - Philosophia Mathematica 13 (2):174-186.
Tennenbaum's Theorem and Unary Functions.Sakae Yaegasi - 2008 - Notre Dame Journal of Formal Logic 49 (2):177-183.

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References found in this work

On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
Bounded existential induction.George Wilmers - 1985 - Journal of Symbolic Logic 50 (1):72-90.
Diophantine Induction.Richard Kaye - 1990 - Annals of Pure and Applied Logic 46 (1):1-40.

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