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Explore a mathematical talk that delves into the separation of levels of Dependent Choice (DC) on reals from levels of Projective Determinacy (PD). Learn about a recent breakthrough in set theory that builds upon the work of Friedman, Gitman, and Kanovei, demonstrating that the Axiom of Choice (AC) does not imply DC in second-order arithmetic. Discover how the speaker and collaborator Sandra Müller modified this construction to create a model of Zermelo-Fraenkel set theory (ZF) where Pi^1_n-determinacy holds for a given n, while Pi^1_k dependent choice for real numbers fails for a specific value of k. Gain insights into the use of Jensen's Diamond Principle and symmetric extensions of L in this construction. This 46-minute presentation, part of the Workshop on "Determinacy, Inner Models and Forcing Axioms" at the Erwin Schrödinger International Institute for Mathematics and Physics, offers a deep dive into advanced topics in set theory and mathematical logic.
