16 citations · 87 across the 24 of their papers we have counts for
7 papers · 1 filter
Preserving the Ultrapower Axiom by Forcing over Nonoverlapping Extender Models
Eyal Kaplan
We identify a class of simple yet nontrivial forcing notions that preserve the Ultrapower Axiom (UA) over canonical inner models, reaching the level of a strong cardinal. The forci…
A note on the Ketonen order and Lipschitz reducibility between ultrafilters
Eyal Kaplan
In his study of the Ultrapower Axiom (UA), Goldberg revealed a connection between UA and the determinacy of certain games that witness Lipschitz reducibility between ultrafilters.…
The number of normal measures, revisited
Eyal Kaplan
We present a new version of the Friedman-Magidor theorem: for every measurable cardinal and , there exists a forcing extension such that any norm…
On fresh sets in iterations of Prikry type forcing notions
Moti Gitik, Eyal Kaplan
We examine the existence (and mostly non-existence) of fresh sets in commonly used iterations of Prikry type forcing notions. Results of [4] are generalized. As an application, a q…
On Easton support iteration of Prikry type forcing notions
Moti Gitik, Eyal Kaplan
We consider here Easton support iterations of Prikry type forcing notions. New ways of constructing normal ultrafilters in extensions are presented. It turns out that, in contrast…
The Magidor Iteration and Restrictions of Ultrapowers to the Ground Model
Eyal Kaplan
We study the Magidor iteration of Prikry forcings below a measurable limit of measurables . We first characterize all the normal measures carries in the generic extension,…
Non-stationary support iterations of Prikry Forcings and Restrictions of Ultrapower Embeddings to the Ground Model
Moti Gitik, Eyal Kaplan
We study the nonstationary-support iteration of Prikry forcings below a measurable cardinal κ, characterizing all the normal measures it carries in the generic extension. We then a…