Mervyn Tong (University of Leeds)

This is the second and final talk in this survey of the Axiom of Determinacy (AD) and its implications on large cardinals. In the first talk, we looked at some first properties of AD and defined the cardinal Θ, which will play a prominent role in the rest of this series. In this talk, we will begin by defining some large cardinal properties — properties that cannot be provably exhibited by cardinals under ZFC — measurability, strong compactness, and supercompactness. We will then state results by Solovay which show that under ZF + AD (or its stronger counterpart ZF + AD_R), ω₁ satisfies these properties at least partially. We will sketch proofs for some (time permitting, all) of these results.