9 found
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  1.  2
    More on Wadge Determinacy.Alessandro Andretta - 2006 - Annals of Pure and Applied Logic 144 (1):2-32.
    We show that the semi-linear ordering principle for continuous functions implies the determinacy of all Wadge and Lipschitz games.
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  2.  3
    Equivalence Between Wadge and Lipschitz Determinacy.Alessandro Andretta - 2003 - Annals of Pure and Applied Logic 123 (1-3):163-192.
    We prove that the determinacy of all Lipschitz games, the determinacy of all Wadge games, and the semi-linear ordering principle for Lipschitz maps are all equivalent.
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  3.  17
    The Iterability Hierarchy Above $${{\Mathrm{\Mathsf {I3}}}}$$ I 3.Alessandro Andretta & Vincenzo Dimonte - 2019 - Archive for Mathematical Logic 58 (1-2):77-97.
    In this paper we introduce a new hierarchy of large cardinals between \ and \, the iterability hierarchy, and we prove that every step of it strongly implies the ones below.
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  4.  5
    How to Win Some Simple Iteration Games.Alessandro Andretta & John Steel - 1997 - Annals of Pure and Applied Logic 83 (2):103-164.
    We introduce two new iteration games: the game , which is a strengthening of the weak iteration game, and the game , which is somewhat stronger than but weaker than the full iteration game of length ω1. For a countable M elementarily embeddable in some Vη, with two players I and II, we can show that II wins and that I does not win.
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  5.  10
    Large Cardinals and Iteration Trees of Height Ω.Alessandro Andretta - 1991 - Annals of Pure and Applied Logic 54 (1):1-15.
    In this paper we continue the line of work initiated in “Building iteration trees”. It is shown that the existence of a certain kind of iteration tree of height ω is equivalent to the existence of a cardinal δ that is Woodin with respect to functions in the next admissible.
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  6.  13
    Building Iteration Trees.Alessandro Andretta - 1991 - Journal of Symbolic Logic 56 (4):1369-1384.
    It is shown, assuming the existence of a Woodin cardinal δ, that every tree ordering on some limit ordinal $\lambda < \delta$ with a cofinal branch is the tree ordering of some iteration tree on V.
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  7.  5
    The Iterability Hierarchy Above $${{\Mathrm{\Mathsf {I3}}}}$$I3.Alessandro Andretta & Vincenzo Dimonte - forthcoming - Archive for Mathematical Logic.
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  8.  13
    Effective Cardinals of Boldface Pointclasses.Alessandro Andretta, Greg Hjorth & Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):35-82.
    Assuming AD + DC, we characterize the self-dual boldface pointclasses which are strictly larger than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank [Formula: see text], and those of Wadge rank [Formula: see text] when ξ is limit.
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  9.  11
    Games, Scales, and Suslin Cardinals. The Cabal Seminar, Volume I, Lecture Notes in Logic, Vol. 31.Alessandro Andretta - 2012 - Bulletin of Symbolic Logic 18 (1):122-126.