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Explore the intricacies of Martin's Conjecture and its application to order-preserving functions in this 52-minute lecture from the Workshop on "Determinacy, Inner Models and Forcing Axioms" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the proposed classification of Turing-invariant functions under the Axiom of Determinacy, focusing on the more tractable yet open question of order-preserving functions. Examine the known results for Borel order-preserving functions and discover a novel approach using inner model theory to extend the conjecture beyond the Borel realm. Learn about the joint work of Benjamin Siskind and Patrick Lutz as they push the boundaries of this mathematical frontier, offering new insights into the intersection of order-preserving Martin's Conjecture and Inner Model Theory.
