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Long games and σ-projective sets

Juan P. Aguilera, Sandra Müller & Philipp Schlicht

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

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Mice with finitely many Woodin cardinals from optimal determinacy hypotheses.Sandra Müller, Ralf Schindler & W. Hugh Woodin - 2020 - Journal of Mathematical Logic 20 (Supp01):1950013.details We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. A consequence is (...) Download Export citation Bookmark 6 citations
Analytic determinacy and 0#. [REVIEW]Leo Harrington - 1978 - Journal of Symbolic Logic 43 (4):685 - 693.details Download Export citation Bookmark 40 citations
(1 other version)Optimal proofs of determinacy.Itay Neeman - 1995 - Bulletin of Symbolic Logic 1 (3):327-339.details In this paper I shall present a method for proving determinacy from large cardinals which, in many cases, seems to yield optimal results. One of the main applications extends theorems of Martin, Steel and Woodin about determinacy within the projective hierarchy. The method can also be used to give a new proof of Woodin's theorem about determinacy in L.The reason we look for optimal determinacy proofs is not only vanity. Such proofs serve to tighten the connection between large cardinals and (...) Download Export citation Bookmark 21 citations
Deconstructing inner model theory.Ralf-Dieter Schindler, John Steel & Martin Zeman - 2002 - Journal of Symbolic Logic 67 (2):721-736.details Download Export citation Bookmark 17 citations
(1 other version)Optimal proofs of determinacy II.Itay Neeman - 2002 - Journal of Mathematical Logic 2 (2):227-258.details We present a general lemma which allows proving determinacy from Woodin cardinals. The lemma can be used in many different settings. As a particular application we prove the determinacy of sets in [Formula: see text], n ≥ 1. The assumption we use to prove [Formula: see text] determinacy is optimal in the base theory of [Formula: see text] determinacy. Download Export citation Bookmark 8 citations
Games of length ω1.Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):83-124.details We prove determinacy for open length ω1 games. Going further we introduce, and prove determinacy for, a stronger class of games of length ω1, with payoff conditions involving the entire run, the club filter on ω1, and a sequence of ω1 disjoint stationary subsets of ω1. The determinacy proofs use an iterable model with a class of indiscernible Woodin cardinals, and we show that the games precisely capture the theory of the minimal model for this assumption. Download Export citation Bookmark 3 citations
Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.details Download Export citation Bookmark 161 citations

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