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Determinacy with complicated strategies

Author: Alexander S. Kechris
Journal: Proc. Amer. Math. Soc. 94 (1985), 333-336
MSC: Primary 03E60; Secondary 03E15, 03E45, 03E55
MathSciNet review: 784188
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Abstract: For any class of functions $ \mathfrak{F}$ from $ {\mathbf{R}}$ into $ {\mathbf{R}},\operatorname{AD}(\mathfrak{F}{\text{)}}$ is the assertion that in every two person game on integers one of the two players has a winning strategy in the class $ \mathfrak{F}$. It is shown, in $ ZF + DC + V = L({\mathbf{R}})$, that for any $ \mathfrak{F}$ of cardinality $ < {2^{{\aleph _0}}}$ (i.e. any $ \mathfrak{F}$ which is a surjective image of $ {\mathbf{R}}$) $ \operatorname{AD}(\mathfrak{F})$ implies AD (the Axiom of Determinacy).

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1985 American Mathematical Society

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