Possible Size of an ultrapower of omega

On the cofinality of ultrapowers

All ultrafilters under consideration here are non-principal ultrafilters on the set omega of natural numbers. We are concerned with the possible cofinalities of ultrapowers of omega with respect to such ultrafilters. We show that no cardinal below the groupwise density number g can occur as such a cofinality and that at most one cardinal below the splitting number s can so occur. The proof for s, when combined with a result of Nyikos, gives the additional information that all P_{kappa}-point ultrafilters, for kappa greater than the bounding number b, are nearly coherent.

可测超幂的闭包性质

Closure properties of measurable ultrapowers

本文研究可测超幂在Hamkin“新鲜性”下的闭包性质，揭示其依赖于集合论模型的组合性质，并利用塌缩与平方原则刻画最强与最弱情形，同时推导一致性强度。

Set theory without choice: not everything on cofinality is possible

We prove (ZF+DC) e.g. : if mu =|H(mu)| then mu^+ is regular non measurable. This is in contrast with the results for mu = aleph_{omega} on measurability see Apter Magidor [ApMg]