Journal of Symbolic Logic 85 (3):1124-1146 (2020)

Authors
Douglas Blue
Harvard University
Abstract
We isolate two abstract determinacy theorems for games of length $\omega_1$ from work of Neeman and use them to conclude, from large-cardinal assumptions and an iterability hypothesis in the region of measurable Woodin cardinals thatif the Continuum Hypothesis holds, then all games of length $\omega_1$ which are provably $\Delta_1$ -definable from a universally Baire parameter are determined;all games of length $\omega_1$ with payoff constructible relative to the play are determined; andif the Continuum Hypothesis holds, then there is a model of ${\mathsf{ZFC}}$ containing all reals in which all games of length $\omega_1$ definable from real and ordinal parameters are determined.
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DOI 10.1017/jsl.2020.71
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References found in this work BETA

Suitable Extender Models I.W. Hugh Woodin - 2010 - Journal of Mathematical Logic 10 (1):101-339.
Inner Models in the Region of a Woodin Limit of Woodin Cardinals.Itay Neeman - 2002 - Annals of Pure and Applied Logic 116 (1-3):67-155.
The Canonical Function Game.Paul B. Larson - 2005 - Archive for Mathematical Logic 44 (7):817-827.
Games of Length Ω1.Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):83-124.
The Determinacy of Long Games.Itay Neeman - 2006 - Bulletin of Symbolic Logic 12 (2):299-302.

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