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Among Martin's most notable work are the proofs of analytic determinacy (from the existence of a measurable cardinal), Borel determinacy (from ZFC alone), the proof (with John R. Steel) of projective determinacy (from suitable large cardinal axioms), and his work on Martin's axiom.
He found one of the first applications of large cardinals to algebra by constructing a certain left-invariant total order, called the Dehornoy order, on the braid group.
Indescribable cardinal, a term used in mathematics to describe a certain kind of large cardinal number that is hard to describe in some language Q