# Shezahd Ahmed: Extracting Measures from Strong Partition Cardinals

Monday, September 9 from 3 to 4pm
Room: TBA
Abstract: We say that a cardinal $\kappa$ has the strong partition property if $\kappa\rightarrow(\kappa)^{\kappa}$. A result due to Erd\”os and Rado tells us that strong partition cardinals do not exist if we take choice. However, in the absence of choice, there is a very natural theory in which strong partition cardinals pop up, namely ZF + AD (Zermelo-Fraenkel set theory with the Axiom of Determinacy). In particular, it turns out that $\aleph_1$ is a strong partition cardinal in ZF + AD. In this talk, I will show how one may extract a measure on strong partition cardinals, using $\aleph_1$ as an example. This talk is expository in nature, and the proofs are entirely combinatorial. Time permitting, I will further discuss the link between determinacy and strong partition cardinals.