Some Axioms of Weak Determinacy
نویسنده
چکیده
We consider two-player games of perfect information of length some cardinal κ. It is well-known that for κ ≥ ω1 the full axiom of determinacy for these games fails, thus we investigate three weaker forms of it. We obtain the measurability of κ under DCκ-the axiom of dependent choices generalized to κ. We generalize the notions of perfect and meager sets and provide characterizations with some special kinds of games. We show that under an additional assumption one of our three axioms follows from the other two.
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