Non-Galvin Filters

We address the question of the consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions \cite[Questions 7.8,7.9]{TomMotiII}, \cite[Question 5]{NegGalSing} and improve theorem \cite[Theorem 2.3]{NegGalSing}

On ω\omega-Strongly Measurable Cardinals

We prove several consistency results concerning the notion of $\omega$-strongly measurable cardinal in HOD. In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than $o(\kappa) = \kappa$, that every successor of a regular cardinal is $\omega$-strongly measurable in HOD

One Repeat Point Gives a Closed, Unbounded Ultrafilter on {\omega_1}

It is shown that the consistency strength of ZF + DC + "the closed unbounded ultrafilter on omega_1 is an ultrafilter" is exactly ZFC + one measurable cardinal.Comment: I apologize for the fact that this is not ready for publication. I've gone back to revise it several times, and each time got distracted by something new. I've decided that it is better to at least make it available in its current for