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Archive for Mathematical Logic

, Volume 28, Issue 2, pp 91–98 | Cite as

On the structure of initial segments of models of arithmetic

  • Jan Krajíček
  • Pavel Pudlák
Article

Abstract

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

Keywords

Mathematical Logic Initial Segment Strong Fragment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Jan Krajíček
    • 1
  • Pavel Pudlák
    • 1
  1. 1.Mathematical InstituteCzechoslovak Academy of SciencesPraha 1Czechoslovakia

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