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


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\( \leqq 2^{a^c } \).


Mathematical Logic Initial Segment Strong Fragment 
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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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