Types of Game That Are Determined
Not all games require the axiom of determinacy to prove them determined. Games whose winning sets are closed are determined. These correspond to many naturally defined infinite games. It was shown in 1975 by Donald A. Martin that games whose winning set is a Borel set are determined. It follows from the existence of sufficient large cardinals that all games with winning set a projective set are determined (see Projective determinacy), and that AD holds in L(R).
Read more about this topic: Axiom Of Determinacy
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