The Limit of Determinacy in Second Order Logic

Explore the precise boundaries of determinacy provable within second-order arithmetic through this 42-minute conference talk that delves into joint research with Richard A. Shore. Examine how n-admissible ordinals and advanced techniques from higher computability theory are essential tools for establishing the exact amount of determinacy that can be demonstrated in second-order arithmetic. Learn about the intricate mathematical framework connecting determinacy theory with higher computability, focusing on the specific role that n-admissible ordinals play in the proof structure. Discover the intersection of reverse mathematics and computability theory as applied to fundamental questions about the limits of what can be proven regarding determinacy in formal mathematical systems.