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Juan P. Aguilera [7]Juan Pablo Aguilera [1]
  1.  24
    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.  8
    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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  3.  9
    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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  4.  4
    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.  6
    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.  6
    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.  12
    Strong Completeness of Provability Logic for Ordinal Spaces.Juan P. Aguilera & David Fernández-Duque - 2017 - Journal of Symbolic Logic 82 (2):608-628.
  8.  6
    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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