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Juan P. Aguilera [8]Juan Pablo Aguilera [1]
  1.  51
    Unsound inferences make proofs shorter.Juan P. Aguilera & Matthias Baaz - 2019 - Journal of Symbolic Logic 84 (1):102-122.
    We give examples of calculi that extend Gentzen’s sequent calculusLKby unsound quantifier inferences in such a way that derivations lead only to true sequents, and proofs therein are nonelementarily shorter thanLK-proofs.
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  2.  24
    Long games and σ-projective sets.Juan P. Aguilera, Sandra Müller & Philipp Schlicht - 2021 - Annals of Pure and Applied Logic 172 (4):102939.
    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 (...)
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  3.  18
    Strong completeness of provability logic for ordinal spaces.Juan P. Aguilera & David Fernández-Duque - 2017 - Journal of Symbolic Logic 82 (2):608-628.
  4.  45
    The consistency strength of long projective determinacy.Juan P. Aguilera & Sandra Müller - 2019 - Journal of Symbolic Logic 85 (1):338-366.
    We determine the consistency strength of determinacy for projective games of length ω^2. Our main theorem is that $\Pi _{n + 1}^1$-determinacy for games of length ω^2 implies the existence of a model of set theory with ω + n Woodin cardinals. In a first step, we show that this hypothesis implies that there is a countable set of reals A such that M_n(A), the canonical inner model for n Woodin cardinals constructed over A, satisfies $A = R$ and the (...)
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  5.  18
    Shortening clopen games.Juan P. Aguilera - 2021 - Journal of Symbolic Logic 86 (4):1541-1554.
    For every countable wellordering $\alpha $ greater than $\omega $, it is shown that clopen determinacy for games of length $\alpha $ with moves in $\mathbb {N}$ is equivalent to determinacy for a class of shorter games, but with more complicated payoff. In particular, it is shown that clopen determinacy for games of length $\omega ^2$ is equivalent to $\sigma $ -projective determinacy for games of length $\omega $ and that clopen determinacy for games of length $\omega ^3$ is equivalent (...)
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  6.  18
    The order of reflection.Juan P. Aguilera - 2021 - Journal of Symbolic Logic 86 (4):1555-1583.
    Extending Aanderaa’s classical result that $\pi ^{1}_{1} < \sigma ^{1}_{1}$, we determine the order between any two patterns of iterated $\Sigma ^{1}_{1}$ - and $\Pi ^{1}_{1}$ -reflection on ordinals. We show that this order of linear reflection is a prewellordering of length $\omega ^{\omega }$. This requires considering the relationship between linear and some non-linear reflection patterns, such as $\sigma \wedge \pi $, the pattern of simultaneous $\Sigma ^{1}_{1}$ - and $\Pi ^{1}_{1}$ -reflection. The proofs involve linking the lengths of (...)
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  7.  32
    Projective Games on the Reals.Juan P. Aguilera & Sandra Müller - 2020 - Notre Dame Journal of Formal Logic 61 (4):573-589.
    Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for L, (...)
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  8.  11
    A topological completeness theorem for transfinite provability logic.Juan P. Aguilera - 2023 - Archive for Mathematical Logic 62 (5):751-788.
    We prove a topological completeness theorem for the modal logic $$\textsf{GLP}$$ GLP containing operators $$\{\langle \xi \rangle :\xi \in \textsf{Ord}\}$$ { ⟨ ξ ⟩ : ξ ∈ Ord } intended to capture a wellordered sequence of consistency operators increasing in strength. More specifically, we prove that, given a tall-enough scattered space X, any sentence $$\phi $$ ϕ consistent with $$\textsf{GLP}$$ GLP can be satisfied on a polytopological space based on finitely many Icard topologies constructed over X and corresponding to the (...)
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  9.  16
    Verification logic: An arithmetical interpretation for negative introspection.Juan Pablo Aguilera & David Fernández-Duque - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 1-20.
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