Abstract:
We study the consistency strength of the axioms of determinacy for infinite games on the natural numbers and the real numbers, AD and AD_R respectively, in the context of Kripke-Platek set theory. We see that $\mathsf{KP} + \text{“}\mathbb{R}\text{ exists”} + \mathsf{AD}$ has strength similar to that of $\mathsf{ZF} + \mathsf{AD}$, while $\mathsf{KP} + \text{“}\mathbb{R}\text{ exists”} + \mathsf{AD}_{\mathbb{R}}$ is much weaker than $\mathsf{ZF} + \mathsf{AD}_{\mathbb{R}}$. The talk will be self-contained.
