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On the structure of initial segments of models of arithmetic

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Abstract

For any countable nonstandard modelM of a sufficiently strong fragment of arithmeticT, and any nonstandard numbersa, c εM, M⊨c≦a, there is a modelK ofT which agrees withM up toa and such that inK there is a proof of contradiction inT with Gödel number\( \leqq 2^{a^c } \).

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Authors and Affiliations

  1. Mathematical Institute, Czechoslovak Academy of Sciences, Žitná 25, CS-11567, Praha 1, Czechoslovakia

    Jan Krajíček & Pavel Pudlák

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  1. Jan Krajíček
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  2. Pavel Pudlák
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Krajíček, J., Pudlák, P. On the structure of initial segments of models of arithmetic. Arch Math Logic 28, 91–98 (1989). https://doi.org/10.1007/BF01633984

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  • DOI: https://doi.org/10.1007/BF01633984

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