Relationship between Kanamori-McAloon Principle and Paris-Harrington Theorem

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 ε0 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.

• Type: Conference
• Year: 2009
• Where: CIE
• Authors: Gyesik Lee
• Keywords: Applied Computing, CIE 2009, Kanamori-McAloon Principle, Parametrised Version, Peano Arithmetic