Sep 29 2020

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

September 29, 2020

11:00 AM - 11:50 AM

Zoom

Chicago, IL

## Calendar

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

Sep 23, 2020

Sep 23, 2020