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math.LO2021
Strong downward Löwenheim-Skolem theorems for stationary logics, III -- mixed support iteration
Sakaé Fuchino, André Ottenbreit Maschio Rodrigue, Hiroshi Sakai
Continuing [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]], we further study reflection principles in connection with the Löwenheim-Skolem Theorems of stati…
math.LO2021
The first-order definability of generic large cardinals
Sakaé Fuchino, Hiroshi Sakai
We show that the notions of generic and Laver-generic supercompactness are first-order definable in the language of ZFC. This also holds for generic and Laver-generic (almost) huge…