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Research

Below, you may find a collection of online preprints, separated into six categories.

  1. Proof Theory. This includes work on dilators and Pi12-logic, finitary and infinitary proof systems, complexity, and cut elimination.
     
  2. Recursion Theory. This includes work in Reverse Mathematics and generalized computability, including inductive definability, admissibility theory, and notions of recursive largeness for ordinals, such as second-order reflection.
     
  3. Set Theory. This includes work on descriptive set theory, inner model theory, determinacy, large cardinals, and forcing.
     
  4. Model Theory. This includes work involving completeness theorems, Löwenheim-Skolem theorems, Hanf numbers, and related notions.
     
  5. Logic in Computer Science. This includes work on many-valued and modal logics, especially from the points of view of complexity and expressibility and of applications to artificial intelligence.
     
  6. Other work. This includes all work not fitting into any of the categories above.
     

Research articles in Proof Theory

  • Recursively Provable Dilators (with Anton Freund and Fedor Pakhomov).
    Submitted for publication.
     
  • Induction on Dilators and Bachmann-Howard Fixed Points (with Anton Freund and Andreas Weiermann).
    Submitted for publication.
     
  • On Some Subtheories of Strong Dependent Choice (with Yudai Suzuki and Keita Yokoyama).
    Submitted for publication.
     
  • Intuitionistic Gödel-Lob Without Sharps (with Leonardo Pacheco).
    Submitted for publication.
     
  • Strong Completeness of the Closed Fragment of GLP (with Grigorii Stepanov), in
    Proceedings of Advances in Modal Logic 2024 (AiML2024).
     
  • Non-linearities in the Analytical Hierarchy (with Fedor Pakhomov).
    Submitted for publication.
     
  • The Logic of Correct Models (with Fedor Pakhomov).
    J. Math. Log., in press.
      
  • The Spectrum of Π13 Soundness (with Fedor Pakhomov).
    Phil. Trans. Roy. Soc. A 381 (2023). Article number 20220013.
      
  • Functorial Fast-Growing Hierarchies (with Fedor Pakhomov and Andreas Weiermann).
    Forum Math. Sigma 12 (2024), pp. 1-16.
     
  • The Π12 Consequences of a Theory (with Fedor Pakhomov).
    J. London Math. Soc. 107 (2023), pp. 1045-1073.
     
  • Ackermann and Goodstein Go Functorial (with Anton Freund, Michael Rathjen, and Andreas Weiermann).
    Pacific J. Math. 313 (2021), pp. 251-291.
     
  • The Number of Axioms (with Matthias Baaz and Jan Bydžovský).
    Ann. Pure Appl. Logic, 173 (2022). Article number 103078.
     
  • A Topological Completeness Theorem for Transfinite Provability Logic.  
    Arch. Math. Logic 62 (2022), pp. 751–788.
     
  • Determinate Logic and the Axiom of Choice.
    Ann. Pure Appl. Logic 171 (2020). Article number 102745.
     
  • Unsound Inferences Make Proofs Shorter (with Matthias Baaz).   
    J. Symbolic Logic 84 (2019), pp. 102-122.
     
  • Strong Completeness of Provability Logic for Ordinal Spaces (with David Fernández-Duque).    
    J. Symbolic Logic 82 (2017), pp. 608-628.

Research articles in Recursion Theory

  • The Limits of Determinacy in Higher-Order Arithmetic (with Thibaut Kouptchinsky).
    Submitted for publication.
     
  • On Winning Strategies for Fσ Games (with Robert Lubarsky).
    J. Symbolic Logic, in press.
     
  • Higher-Order Feedback Computation (with Robert Lubarsky and Leonardo Pacheco), in Proceedings of Computability in Europe 2024 (CiE2024).
     
  • The Metamathematics of Separated Determinacy.
    Invent. Math. 240 (2025), pp. 313-457.
     
  • Determinacy on the Edge of Second-Order Arithmetic (with Philip Welch).
    Submitted for publication.
     
  • Type-2 Feedback Computability (with Martín Soto).
    Computability, in press.
      
  • Locally Hyperarithmetical Induction.
    Bull. London Math. Soc. 55 (2023), pp. 865-878.
      
  • A proof of Grilliot's Theorem (with Ferre Vanden Kerchove).
    Bull. Belgian Math. Soc. 31 (2024), pp. 1-16.
     
  • Effective Cardinals and Σ04-Determinacy.
    J. Symbolic Logic, in press.
     
  • Feedback Hyperjump (with Robert Lubarsky).
    J. Log. Comput. 31 (2021), pp. 20-39.
     
  • A Characterization of Σ11-Reflecting Ordinals.
    Ann. Pure Appl. Logic 172 (2021). Article number 103009.
     
  • The Order of Reflection.
    J. Symbolic Logic 86 (2021), pp. 1555-1583.

Research articles in Set Theory

  • The Complexity of Wellordered- and Scattered-Convex Embeddability (with Martina Iannella).
    Submitted for publication.
     
  • Large Cardinals, Structural Reflection, and the HOD Conjecture (with Joan Bagaria and Philipp Lücke).
    Submitted for publication.

    Read perspectives on this work for general audiences at [New Scientist], [IFLScience], [Popular Mechanics], [MaddMaths (in Italian)], [WIRED magazine (in Italian)], [WIRED magazine (in Spanish)], [muy interesante (in Spanish)], [Deutsche Welle (in Spanish)], [El Cronista (in Spanish)], [AOL news], [Yahoo! news], [xataka (in Spanish)], [Correio Braziliense (in Portuguese)], [ZME Science].
      
  • Determinacy from Sharps.
    Israel J. Math., in press.
     
  • A one-page proof of a theorem of Beleznay (with Martina Iannella).
    Bull. Symbolic Logic, in press.
     
  • Reflection Properties of Ordinals in Generic Extensions (with Corey Switzer).
    Submitted for publication.
      
  • Monotone versus Non-Monotone Projective Operators (with Philip Welch).
    Bull. London Math. Soc., in press.
     
  • Recursively Large Projective Ordinals.
    Submitted for publication.
     
  • σ-Projective Sets of Reals, Cut Elimination, and Large Cardinals.
    Internat. Math. Nachrichten 248 (2021), pp. 17-27.
     
  • Boundedness Theorems for Flowers and Sharps (with Anton Freund, Michael Rathjen, and Andreas Weiermann).
    Proc. Amer. Math. Soc. 150 (2022), pp. 3973-3988.
     
  • Countable Ordinals in Indiscernibility Spectra.
    Fund. Math. 260 (2023), pp. 99-109.
     
  • Gδσ Games and Induction on Reals (with Philip Welch).
    J. Symbolic Logic 86 (2021). pp. 1676-1690.
     
  • Projective Games on the Reals (with Sandra Müller).
    Notre Dame J. Form. Log. 64 (2020) pp. 573–589.
     
  • Provably Δ1 Games (with Douglas Blue).
    J. Symbolic Logic 85 (2020), pp. 1124–1146.
     
  • Fσ Games and Reflection in L(R).
    J. Symbolic Logic 85 (2020), pp. 1102–1123.
     
  • Long Borel Games.
    Israel J. Math 243 (2021), pp.273-314.
     
  • Shortening Clopen Games.
    J. Symbolic Logic 86 (2021), pp. 1541-1554.
     
  • Determined Admissible Sets.
    Proc. Amer. Math. Soc. 148 (2020), pp. 2217-2231.
     
  • The Consistency Strength of Long Projective Determinacy (with Sandra Müller).
    J. Symbolic Logic 85 (2020), pp. 338-366.
     
  • Long Games and σ-Projective Sets (with Sandra Müller and Philipp Schlicht).
    Ann. Pure Appl. Logic 172 (2021). Article number 102939.
     
  • σ-Projective Determinacy.
    Submitted for publication.

Research articles in Model Theory

  • Local Hanf-Tarski Numbers.
    Submitted for publication.
     
  • Boolean Completeness of Infinitary Logic with Arbitrary Signatures.
    Submitted for publication.
     
  • The Compactness of Gödel Logic.
    J. Symbolic Logic, in press.
     
  • The Löwenheim-Skolem Theorem for Gödel Logic.
    Ann. Pure Appl. Logic 174 (2023). Article number 103235.
     

Research articles in Logic in Computer Science


  • Constructive Quantum Logics (with Guillaume Massas).
    Submitted for publication.
     
  • Intuitionistic Gödel-Lob Without Sharps (with Leonardo Pacheco).
    Submitted for publication.
     
  • Gödel-Dummett Linear Temporal Logic (with Martin Diéguez, David Fernandez-Duque and Brett McLean).
    Artif. Intell. 338 (2025), article number 104236.

    This is an extended version of the articles:
    A Gödel Calculus for Linear Temporal Logic (with Martin Diéguez, David Fernandez-Duque and Brett McLean), in Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR 2022); and
    Time and Gödel: Fuzzy Temporal Reasoning in PSPACE (with Martin Diéguez, David Fernandez-Duque and Brett McLean) in Proceedings of the Workshop on Logic, Language, Information, and Computation (WoLLIC 2022).
     
  • Fundamental Logic is Decidable (with Jan Bydžovský).
    ACM Trans. Comp. Logic 25 (2024), pp. 1-14.
      
  • Noetherian Gödel Logics (with Jan Bydžovský and David Fernández-Duque).  
    J. Log. Comp., 32 (2022), pp. 1487–1503.

    This is an extended version of the article:
    A non-hyperarithmetical Gödel logic (with Jan Bydžovský and David Fernández-Duque), in Proceedings of the Conference on Logical Foundations of Computer Science (LFCS 2021).
     
  • Verification Logic (with David Fernández-Duque).    
    J. Log. Comp.     27 (2017), pp. 2451-2469.

    This is an extended version of the article:
    An arithmetical interpretation for negative introspection (with David Fernández-Duque), in Proceedings of Advances in Modal Logic (AiML 2016).
      
  • Ten Problems in Gödel Logic (with Matthias Baaz).    
    Soft Comput.     21 (2017), pp. 149-152.

Other research articles

  • On the Maximization of Menu-Dependent Interval Orders (with Levent Ülkü).  
    S. Choice Welf. 48 (2017), pp. 357-366. 

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