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CIE
2009
Springer

Relationship between Kanamori-McAloon Principle and Paris-Harrington Theorem

8 years 6 months ago
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.
Gyesik Lee
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CIE
Authors Gyesik Lee
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