7 papers · 1 filter
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…
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…
Strong downward Löwenheim-Skolem theorems for stationary logics, II -- reflection down to the continuum
Sakaé Fuchino, André Ottenbreit Maschio Rodrigues, Hiroshi Sakai
Continuing the previous paper, we study the Strong Downward Löwenheim-Skolem Theorems (SDLSs) of the stationary logic and their variations. It has been shown that the SDLS for the…
Martin's Maximum and the Diagonal Reflection Principle
Sean Cox, Hiroshi Sakai
We prove that Martin's Maximum does not imply the Diagonal Reflection Principle for stationary subsets of .
A variant of Shelah's characterization of Strong Chang's Conjecture
Sean Cox, Hiroshi Sakai
Shelah considered a certain version of Strong Chang's Conjecture, which we denote , and proved that it is equivalent to several statements, including the a…
The weakly compact reflection principle need not imply a high order of weak compactness
Brent Cody, Hiroshi Sakai
The weakly compact reflection principle states that is a weakly compact cardinal and every weakly compact subset of has a weakly compact proper…