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. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Lee, G. (2009). Relationship between Kanamori-McAloon principle and Paris-Harrington theorem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5635 LNCS, pp. 310–323). https://doi.org/10.1007/978-3-642-03073-4_32
Mendeley helps you to discover research relevant for your work.