Determinacy for Games Ending at the First Admissible Relative to the Play

Journal of Symbolic Logic 71 (2):425 - 459 (2006)
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Let o(κ) denote the Mitchell order of κ. We show how to reduce long games which run to the first ordinal admissible in the play, to iteration games on models with a cardinal κ so that (1) κ is a limit of Woodin cardinals: and (2) o(κ) = κ⁺⁺. We use the reduction to derive several optimal determinacy results on games which run to the first admissible in the play



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Inner models with many Woodin cardinals.J. R. Steel - 1993 - Annals of Pure and Applied Logic 65 (2):185-209.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Unraveling Π11 sets.Itay Neeman - 2000 - Annals of Pure and Applied Logic 106 (1-3):151-205.
Determinacy in the Mitchell models.John R. Steel - 1982 - Annals of Mathematical Logic 22 (2):109.

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