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 \(T_2\) “weak” principles do not imply “strong” ones.
On the relative strength of finitary combinatorial principles
14.12.2017 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25