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Separations of first and second order theories in bounded arithmetic

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Abstract

We prove that PTC N (n) (the polynomial time closure of the nonstandard natural number n in the model N of S2.) cannot be a model of U12. This implies that there exists a first order sentence of bounded arithmetic which is provable in U12 but does not hold in PTC N (n).

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  1. Graduate School of Informatics, Nagoya University, Nagoya, 464-8601, Japan

    Masahiro Yasumoto

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  1. Masahiro Yasumoto
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Correspondence to Masahiro Yasumoto.

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Yasumoto, M. Separations of first and second order theories in bounded arithmetic. Arch. Math. Logic 44, 685–688 (2005). https://doi.org/10.1007/s00153-005-0281-3

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  • DOI: https://doi.org/10.1007/s00153-005-0281-3

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