March 22
Sakae Fuchino,
Kobe University
A Löwenheim-Skolem Theorem for a variation of stationary logic which implies that the continuum is very large
We consider three variations of the Löwenheim-Skolem Theorem type statements on stationary logics. These statements imply respectively that the size of the continuum is $\aleph_1$, $\aleph_2$ or very big (e.g. hyper, hyper, ... weakly Mahlo).
We also consider reflection principles in terms of games and strengthenings of generic supercompactness which are related to these three Löwenheim-Skolem Theorems for stationary logics.