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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 logics and modal logics, especially from the point of view of complexity and expressibility.
     
  6. Other work. This includes all work not fitting into any of the categories above.
     

Research articles in Proof Theory


  • 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).
    Submitted for publication.
     
  • 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 Metamathematics of Separated Determinacy.
    Submitted for publication, 122pp.
     
  • Determinacy on the Edge of Second-Order Arithmetic (with Philip Welch).
    Submitted for publication, 92pp.
     
  • Type-2 Feedback Computability (with Martín Soto).
    Submitted for publication.
      
  • 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., in press.
     
  • 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

  • Reflection Properties of Ordinals in Generic Extensions (with Corey Switzer).
    Submitted for publication.
     
  • Monotone versus Non-Monotone Projective Operators (with Philip Welch).
    Submitted for publication.
     
  • 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

  • The Compactness of Gödel Logic.
    Submitted for publication.
     
  • The Löwenheim-Skolem Theorem for Gödel Logic.
    Ann. Pure Appl. Logic 174 (2023). Article number 103235.
     

Research articles in Logic in Computer Science


  • Gödel-Dummett Linear Temporal Logic (with Martin Diéguez, David Fernandez-Duque and Brett McLean).
    Submitted for publication.
    See also: A Gödel Calculus for Linear Temporal Logic in Proceedings of KR 2022 and Time and Gödel: Fuzzy Temporal Reasoning in PSPACE in Proceedings of WoLLIC 2022.
     
  • Fundamental Logic is Decidable (with Jan Bydžovský).
    ACM Trans. Comp. Logic, in press.
      
  • Noetherian Gödel Logics (with Jan Bydžovský and David Fernández-Duque).  
    J. Log. Comp., 32 (2022), pp. 1487–1503.
    See also: A non-hyperarithmetical Gödel logic in Proceedings of LFCS 2021.
     
  • Verification Logic (with David Fernández-Duque).    
    J. Log. Comp.     27 (2017), pp. 2451-2469.
    See also: An arithmetical interpretation for negative introspection in Proceedings of 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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