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Relationship between Kanamori-McAloon Principle and Paris-Harrington Theorem

  • Gyesik Lee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5635)

Abstract

We give a combinatorial proof of a tight relationship between the Kanamori-McAloon principle and the Paris-Harrington theorem with a number-theoretic parameter function. We show that the provability of the parametrised version of the Kanamori-McAloon principle can exactly correspond to the relationship between Peano Arithmetic and the ordinal ε 0 which stands for the proof-theoretic strength of Peano Arithmetic. Because A. Weiermann already noticed the same behaviour of the parametrised version of Paris-Harrington theorem, this indicates that both propositions behave in the same way with respect to the provability in Peano Arithmetic.

Keywords

Kanamori-McAloon principle Paris-Harrington theorem Peano Arithmetic independence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gyesik Lee
    • 1
  1. 1.ROSAEC centerSeoul National UniversitySeoulKorea

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