Martin's measurable dilator

Abstract

Martin's remarkable proof of ${\hat{\mathbf{I}}}_2^1$-determinacy from an iterable rank-into-rank embedding highlighted the connection between large cardinals and determinacy. In this paper, we isolate a large cardinal object called a measurable dilator from Martin's proof of ${\hat{\mathbf{I}}}_2^1$-determinacy, which captures the structural essence of Martin's proof of ${\hat{\mathbf{I}}}_2^1$-determinacy.

46 pages, Revised subsections for dendrograms and Section 6