A connection between decomposable ultrafilters and possible cofinalities. II

A connection between decomposability of ultrafilters and possible cofinalities

We introduce the decomposability spectrum $K_D=\{λ\geq ω| D \text{is} λ\text{-decomposable}\}$ of an ultrafilter $D$, and show that Shelah's $\pcf$ theory influences the possible values $K_D$ can take. For example, we show that if $\aaa$ is a set of regular cardinals, $μ\in \pcfa$, the ultrafilter $D$ is $|\aaa |^+$-complete and $K_D \subseteq \aaa$, then $μ\in K_D$. As a consequence, we show that if $ λ$ is singular and for some $ λ' < λ$ $K_D$ contains all regular cardinals in $ [λ', λ)$ then: (a) if $\cf λ= ω$ then either $ λ\in K_D$, or $ λ^+ \in K_D$; and (b) if $D$ is $(\cf λ)^+$-complet…

线性序超积中截的共尾数的数量研究

On the number of cofinalities of cuts in ultraproducts of linear orders

该研究以正则基数κ及非递减正则基数序列为对象，探究线性序超积中截的可能共尾数集合的构成，明确不同超滤下截共尾数的存在情况。

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.

可测基数上Rudin-Keisler顺序的定向性

The directedness of the Rudin-Keisler order at measurable cardinals

本文研究了可测基数上Rudin-Keisler顺序的定向性，证明了在ZFC下某些理论的等一致性和首次展示了在可测基数层面的紧致性性质的一致性强度低于强基数。