Most of the regularity properties of ideals introduced by Taylor are equivalent at successor cardinals. For $\kappa = \mu^+$ with $\mathrm{cf}(\mu)$ uncountable, we can rid the universe of dense ideals on $\mathcal{P}_\kappa(\lambda)$ for while preserving nonregular ideals on the same set.

Many consistency results in set theory involve forcing over a universe V0 that contains a large cardinal to get a model V1. The original large cardinal embedding is then extended generically using a… Expand

Introduction. In the theory of models, the ultraproduct (or prime reduced product) construction has been a very useful method of forming models with given properties (see, for instance, [2]). I t is… Expand

In this paper we consider whether the minimal normal filter onPκλ, the club filter, can have strong properties like saturation, pre-saturation, or cardinal preserving. We prove in a number of cases… Expand

Let κ be a singular cardinal in V , and let W ⊇ V be a model such that κ+V = λ + W for some W -cardinal λ with W |= cf(κ) 6= cf(λ). We apply Shelah’s pcf theory to study this situation, and prove the… Expand

Author(s): Eskew, Monroe Blake | Advisor(s): Zeman, Martin | Abstract: Ulam proved that there cannot exist a probability measure on the reals for which every set is measurable and gets either measure… Expand