Kurt Gödel Research Center

2017 seminar talk: On the relative strength of finitary combinatorial principles

Talk held by Moritz Müller (KGRC) at the KGRC seminar on 2017-12-14.

Abstract

Define a finitary combinatorial principle to be a first-order sentence which is valid in the finite but falsifiable in the infinite. We aim to compare the strength of such principles over a weak arithmetic. We distinguish “weak” and “strong” principles based on their behaviour with respect to finite structures that are only partially defined. The talk sketches a forcing proof of a theorem stating that over relativized $T^1_2$ “weak” principles do not imply “strong” ones.