Turing Determinacy and Suslin sets

Abstract

The relationship between the Axiom of Determinacy (AD) and the Axiom of Turing Determinacy has been open for over 50 years, and the attempts to understand that relationship has had a profound influence on Set Theory in a variety of ways. The prevailing conjecture is that these two determinacy hypotheses are actually equivalent, and the main theorem of this paper is that Turing Determinacy implies that every Suslin set is determined.