Anton Freund

I am a PhD student at the University of Leeds, supervised by Michael Rathjen.

Email: A.J.Freund14[at]leeds[dot]ac[dot]uk

Research Interests:

  • 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  • A Uniform Characterization of Γ1-Reflection over the Fragments of Peano Arithmetic, unpublished note, 2015.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.

Selected Talks:

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