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Explore the structural properties of simply definable sets at higher cardinals in this 41-minute conference talk from the Workshop on "Reverse Mathematics and Higher Computability Theory" at the Erwin Schrödinger International Institute. Discover how the canonical structure theory of simply definable sets of real numbers has motivated set theorists to investigate similar concepts at higher cardinalities. Learn about recent research demonstrating that structural properties of definable sets of low complexity at higher cardinals closely mirror the combinatorial properties of these cardinals themselves. Examine joint work with Omer Ben-Neria from Jerusalem that employs definability techniques to analyze the extent of Ramsey-theoretic properties of singular cardinals, providing new insights into the intersection of descriptive set theory, cardinal arithmetic, and combinatorial properties of large cardinals.
