Logic Seminar
Spencer Unger
UCLA
The tree property and weak square
Abstract: In this talk we focus on generalizing two theorems of Mitchell, but in different directions. The theorems of Mitchell are
Thm 1: The tree property at $\aleph_2$ is equiconsistent with the existence of weakly compact cardinal.
Thm 2: The failure of weak $\square_{\aleph_1}$ is equiconsistent with a Mahlo cardinal.
We develop some of the tools needed to prove the following two theorems.
Thm1': Assuming there is a weakly compact cardinal it is consistent that the tree property holds at $\aleph_2$ and the continuum is larger than $\aleph_2$.
Thm2': The failure of weak $\square_{\aleph_n}$ for all n > 0 is equiconsistent with infinitely many Mahlo cardinals.
Tuesday October 8, 2013 at 4:00 PM in SEO 427