Anatomy of $\tilde{\mathbb{E}}$

Abstract

We present a detailed general framework to describe the forcing $\tilde{\mathbb{E}}$, defined by Kellner, Shelah and Tanăsie to prove the consistency with ZFC of an alternative order of Cichoń's maximum. Our presentation is close to the framework of tree-creature forcing notions from Horowitz and Shelah. We show that the posets in this class have strong FAM limits for intervals (in recent terminology, they are $\sigma$-FAM-linked) and, furthermore, that they also have strong ultrafilter limits for intervals.

To appear in RIMS Kôkyûroku, Kyoto University