- Foundations of mathematics, especially meta-mathematics of arithmetic (first and second order) and weak set theories
- Higher-order aspects of proof-theoretic concepts
- Computational content of proofs, program extraction
- Length of proofs, slow consistency
- Methods: Mainly ordinal analysis, but also set-theoretic constructions and non-standard models of arithmetic
Papers and Notes:
- Short Proofs for Slow Consistency, with Fedor Pakhomov, submitted. Preprint available via arXiv:1712.03251.
- A Note on Iterated Consistency and Infinite Proofs, submitted. Preprint available via arXiv:1709.01540.
- A Higher Bachmann-Howard Principle. Preprint available via arXiv:1704.01662.
- Slow Reflection, Ann. Pure Appl. Logic 168(12) 2017, pp. 2103-2128. Available via doi:10.1016/j.apal.2017.06.003 (journal version) or arXiv:1601.08214 (accepted manuscript).
- Proof Lengths for Instances of the Paris-Harrington Principle, Ann. Pure Appl. Logic 168(7) 2017, pp. 1361-1382. Available via doi:10.1016/j.apal.2017.01.004 (journal version) or arXiv:1601.08185 (accepted manuscript).
- A Uniform Characterization of Γ1-Reflection over the Fragments of Peano Arithmetic, unpublished note, 2015. Available via arXiv:1512.05122.
- Lattice-based and topological representations of binary relations with an application to music, with M. Andreatta and J.-L. Giavitto, Ann. Math. Artif. Intell. 73(3-4) 2015, pp. 311-334. Available via doi:10.1007/s10472-014-9445-3.
- Characteristic Spaces of del Pezzo Surfaces, Master's Thesis at LMU Munich, 2014. Supervised by Ulrich Derenthal, and available via his website.
- Proof Length and the Paris-Harrington Principle, Oberwolfach Workshop "Mathematical Logic: Proof Theory, Constructive Mathematics", 2017. Extended abstract to appear in the Oberwolfach Reports series.
- Type-Two Well-Ordering Principles and Π11-Comprehension, invited to the special session on proof theory, Logic Colloquium 2017, Stockholm University. Abstract to appear in Bull. Symbolic Logic.
- The slow reflection hierarchy, Logic Colloquium 2016, University of Leeds. Abstract in Bull. Symbolic Logic 23(2) 2017, pp. 240-241. Available via doi:10.1017/bsl.2017.16.
- A computational look at slow provability, Workshop Mathematics for Computation, Niederalteich 2016.
- Where can we really prove instances of the Paris-Harrington Principle?, Joint DMV and GAMM Annual Meeting 2016, TU Braunschweig. Extended abstract in Proc. Appl. Math. Mech. 16 (2016), pp. 903-904. Available via doi:10.1002/pamm.201610440.
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