Nairian Models - Axiom of Determinacy and Forcing the Axiom of Choice

Explore advanced set theory concepts in this 53-minute mathematical lecture that introduces Nairian Models, which are models of the Axiom of Determinacy featuring non-trivial structure above their Theta. Learn how to force the Axiom of Choice over these models and discover why the square principle fails in the resulting generic extensions. Examine various combinatorial principles that hold in these extensions of Nairian Models, with insights drawn from collaborative research with Douglas Blue and Paul Larson. Gain understanding of sophisticated mathematical structures at the intersection of set theory, forcing techniques, and determinacy axioms through detailed explanations of these specialized models and their properties.