1. On the Notion of Guessing Model.Matteo Viale - forthcoming - Annals of Pure and Applied Logic.
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    Martin’s Maximum Revisited.Matteo Viale - 2016 - Archive for Mathematical Logic 55 (1-2):295-317.
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  3. The Cumulative Hierarchy and the Constructible Universe of ZFA.Matteo Viale - 2004 - Mathematical Logic Quarterly 50 (1):99.
    We present two results which shed some more light on the deep connection between ZFA and the standard ZF set theory: First of all we refine a result of Forti and Honsell in order to prove that the universe of ZFA can also be obtained as the least fixed point of a continuous operator and not only as the greatest fixed point of the powerset operator. Next we show that it is possible to define a new absolute Gödel operation in (...)
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    Guessing Models and Generalized Laver Diamond.Matteo Viale - 2012 - Annals of Pure and Applied Logic 163 (11):1660-1678.
    We analyze the notion of guessing model, a way to assign combinatorial properties to arbitrary regular cardinals. Guessing models can be used, in combination with inaccessibility, to characterize various large cardinal axioms, ranging from supercompactness to rank-to-rank embeddings. The majority of these large cardinal properties can be defined in terms of suitable elementary embeddings j:Vγ→Vλ. One key observation is that such embeddings are uniquely determined by the image structures j[Vγ]≺Vλ. These structures will be the prototypes guessing models. We shall show, (...)
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    The Proper Forcing Axiom and the Singular Cardinal Hypothesis.Matteo Viale - 2006 - Journal of Symbolic Logic 71 (2):473 - 479.
    We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof uses the reflection principle MRP introduced by Moore in [11].
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    Absoluteness Via Resurrection.Giorgio Audrito & Matteo Viale - 2017 - Journal of Mathematical Logic 17 (2):1750005.
    The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Veličković. We introduce a stronger form of resurrection axioms for a class of forcings Γ and a given ordinal α), and show that RAω implies generic absoluteness for the first-order theory of Hγ+ with respect to forcings in Γ preserving the axiom, where γ = γΓ is a cardinal which depends on Γ. We also prove that the consistency strength of these axioms (...)
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    Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics.Matteo Viale - 2008 - Bulletin of Symbolic Logic 14 (1):99-113.