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Explore the fascinating intersection of set theory and large cardinal axioms in this 59-minute conference talk that delves into choiceless large cardinals and their fundamental properties. Examine how large cardinal concepts behave in contexts where the axiom of choice is not assumed, investigating the subtle relationships between determinacy, measurability, and cardinal arithmetic without choice. Discover the technical challenges and surprising results that emerge when classical large cardinal theory is extended to choiceless settings, including discussions of measurable cardinals, strong cardinals, and their variants in models of set theory without the axiom of choice. Learn about the connections between choiceless large cardinals and descriptive set theory, particularly how these concepts relate to determinacy hypotheses and the structure of the real numbers. Gain insights into current research directions and open problems in this specialized area of mathematical logic, presented as part of the ICBS2025 conference series.
