Limit Ultrapowers

Boolean Ultrapowers, the Bukovský-dehornoy Phenomenon, and Iterated Ultrapowers

We show that while the length ω iterated ultrapower by a normal ultrafilter is a Boolean ultrapower by the Boolean algebra of Př́ıkrý forcing, it is consistent that no iteration of length greater than ω (of the same ultrafilter and its images) is a Boolean ultrapower. For longer iterations, where different ultrafilters are used, this is possible, though, and we give Magidor forcing and a general...

Fresh subsets of ultrapowers

In [8], Shelah and Stanley constructed a κ-Aronszjan tree with an ascent path using κ. We show that κ,2 does not imply the existence of Aronszajn trees with ascent paths. The proof goes through an intermediate combinatorial principle, which we investigate further.

On the Cofinality of Ultrapowers

We prove some restrictions on the possible cofinalities of ultrapowers of the natural numbers with respect to ultrafilters on the natural numbers. The restrictions involve two cardinal characteristics of the continuum, the splitting number s and the groupwise density number g.

On Partially Wellfounded Generic Ultrapowers

We construct a model without precipitous ideals but so that for each τ < א3 there is a normal ideal over א1 with generic ultrapower wellfounded up to the image of τ .

Observational Ultrapowers of Polynomial Coalgebras