6 papers
Walks along a weak square sequence and the non-semiproperness of Namba forcings
Kenta Tsukuura
In this paper, we demonstrate that if, for every -complete fine filter over , the associated Namba forcing is semiproper, then $\square(…
On semiproperness of Namba forcings and Ideals in Prikry extensions
Kenta Tsukuura
In this paper, we study some variations of Namba forcing over and show that its semiproperness implies . In particular…
On the centeredness of saturated ideals
Kenta Tsukuura
We show that Kunen's saturated ideal over is not centered. We also evaluate the extent of saturation of Laver's saturated ideal in terms of -saturation.
Prikry-type forcings after collapsing a huge cardinal
Kenta Tsukuura
Some models of combinatorial principles have been obtained by collapsing a huge cardinal in the case of the successors of regular cardinals. For example, saturated ideals, Chang's…
The extent of saturation of induced ideals
Kenta Tsukuura
We construct a model with a saturated ideal over and study the extent of saturation of .
Prikry-type forcing and the set of possible cofinalities
Kenta Tsukuura
It is known that the set of possible cofinalities has good properties if is a progressive interval of regular cardinals. In this paper, we give an interval of…