Annals of Pure and Applied Logic 172 (4):102939 (2021)

Authors
Sandra Eleonore Müller
Ludwig Maximilians Universität, München
Abstract
We prove a number of results on the determinacy of σ-projective sets of reals, i.e., those belonging to the smallest pointclass containing the open sets and closed under complements, countable unions, and projections. We first prove the equivalence between σ-projective determinacy and the determinacy of certain classes of games of variable length <ω^2 (Theorem 2.4). We then give an elementary proof of the determinacy of σ-projective sets from optimal large-cardinal hypotheses (Theorem 4.4). Finally, we show how to generalize the proof to obtain proofs of the determinacy of σ-projective games of a given countable length and of games with payoff in the smallest σ-algebra containing the projective sets, from corresponding assumptions (Theorem 5.1, Theorem 5.4).
Keywords Infinite game  Determinacy  Inner model theory  Large Cardinal  Long game  Mouse
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DOI 10.1016/j.apal.2020.102939
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References found in this work BETA

Analytic Determinacy and 0#. [REVIEW]Leo Harrington - 1978 - Journal of Symbolic Logic 43 (4):685 - 693.
Optimal Proofs of Determinacy.Itay Neeman - 1995 - Bulletin of Symbolic Logic 1 (3):327-339.
Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.

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