Sep 29 2020

Logic Seminar: Weak square from weak presaturation, by Monroe Eskew

September 29, 2020

11:00 AM - 11:50 AM

Location

Zoom

Address

Chicago, IL

Monroe Eskew (KGRC): Weak square from weak presaturation

The motivating question for this work is: Can we have both a saturated ideal and the tree property on $\aleph_2$? Towards the negative direction, we show that for a regular cardinal $\kappa$, if $2^{<\kappa}\leq\kappa^+$ and there is a weakly presaturated ideal on $\kappa^+$ concentrating on cofinality $\kappa$, then $\square^*_\kappa$ holds. This proves a conjecture of Foreman about the approachability ideal on $\aleph_2$ under the assumption that the continuum is at most $\aleph_2$. A surprising corollary is that if there is a weakly presaturated ideal $J$ on $\aleph_2$ such that $P(\aleph_2)/J$ is a proper forcing, then CH holds. This is joint work with Sean Cox. This meeting will be using Zoom - please write an email to fcaldero@uic.edu or sinapova@uic.ed for login information. Please click here to make changes to, or delete, this seminar announcement.

Contact

Filippo Calderoni

Date posted

Sep 23, 2020

Date updated

Sep 23, 2020

Speakers

Monroe Eskew | (KGRC)