Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Determinacy with complicated strategies


Author: Alexander S. Kechris
Journal: Proc. Amer. Math. Soc. 94 (1985), 333-336
MSC: Primary 03E60; Secondary 03E15, 03E45, 03E55
DOI: https://doi.org/10.1090/S0002-9939-1985-0784188-0
MathSciNet review: 784188
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E60, 03E15, 03E45, 03E55

Retrieve articles in all journals with MSC: 03E60, 03E15, 03E45, 03E55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0784188-0
Article copyright: © Copyright 1985 American Mathematical Society