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Long Borel Games

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Abstract

We study games of length ω2 with moves in ℕ and Borel payoff. These are, e.g., games in which two players alternate turns playing digits to produce a real number in [0, 1] infinitely many times, after which the winner is decided in terms of the sequence belonging to a Borel set in the product space [0,1]ℕ.

The main theorem is that Borel games of length ω2 are determined if, and only if, for every countable ordinal α, there is a fine-structural, countably iterable model of Zermelo set theory with α-many iterated powersets above a limit of Woodin cardinals.

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Authors and Affiliations

  1. Department of Mathematics, University of Ghent, Krijgslaan 281-S8, 9000, Ghent, Belgium

    J. P. Aguilera

  2. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria

    J. P. Aguilera

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Aguilera, J.P. Long Borel Games. Isr. J. Math. 243, 273–314 (2021). https://doi.org/10.1007/s11856-021-2160-y

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  • DOI: https://doi.org/10.1007/s11856-021-2160-y

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