Deutsch Intern
Mathematical Logic

Holder of the Junior Professorship

Prof. Dr. Anton Freund

Holder of the Junior Professorship
Junior Professorship at the Chair of Mathematics III (Mathematical Logic)
Emil-Fischer-Straße 40
97074 Würzburg
Building: 40 (Mathematik Ost)
Room: 01.012
Phone: +49 931 31-80576
Portrait Anton Freund

The following links provide information on

  • 2008-14: Bachelor and Master studies at LMU Munich with a gap year in Paris

  • 2014-18: PhD studies with Michael Rathjen at Leeds

  • 2018-21: Postdoc with Ulrich Kohlenbach at Darmstadt

  • 2021-23: Emmy Noether group leader (DFG) at Darmstadt

  • since 2023: Tenure track professor and Emmy Noether group leader at Würzburg

Publications

Lecture notes can be found via the link to teaching material

  • 1.
    Dilators and the reverse mathematics zoo
    Freund, A.
    arXiv preprint, 23 pp (2024)
  • 1.
    Fraïssé’s conjecture, partial impredicativity and well-ordering principles, part I
    Freund, A.
    arXiv preprint, 10 pp (2024)
  • 1.
    Reverse mathematics of a uniform Kruskal-Friedman theorem
    Freund, A.
    arXiv preprint, 25 pp (2021)

  • 1.
    Weak well orders and Fraïssé’s conjecture
    Freund, A., Manca, D.
    The Journal of Symbolic Logic, 16 pp, to appear
  • 1.
    Provable better quasi orders
    Freund, A., Marcone, A., Pakhomov, F., Soldà, G.
    Notre Dame Journal of Formal Logic, 13 pp, to appear
  • 1.
    Higman’s lemma is stronger for better quasi orders
    Freund, A.
    Order, 7 pp, to appear
  • 1.
    The logical strength of minimal bad arrays
    Freund, A., Pakhomov, F., Soldà, G.
    Proceedings of the American Mathematical Society 13 pp, to appear
  • 1.
    Normal functions and maximal order types
    Freund, A., Manca, D.
    Journal of Logic and Computation, 34, 1064-1081 (2024)
  • 1.
    Bachmann-Howard derivatives
    Freund, A.
    Archive for Mathematical Logic 62, 581-618 (2023)
  • 1.
    Bounds for a nonlinear ergodic theorem for Banach spaces
    Freund, A., Kohlenbach, U.
    Ergodic Theory and Dynamical Systems 43, 1570-1593 (2023)
  • 1.
    The uniform Kruskal theorem: between finite combinatorics and strong set existence
    Freund, A., Uftring, P.
    Philosophical Transactions of the Royal Society A 381, article no. 20220016, 16 pp (2023)
  • 1.
    On the logical strength of the better quasi order with three elements
    Freund, A.
    Transactions of the American Mathematical Society 376, 6709–6727 (2023)
  • 1.
    Well ordering principles for iterated Pi^1_1-comprehension
    Freund, A., Rathjen, M.
    Selecta Mathematica 29, article no. 76, 83 pp (2023)
  • 1.
    Minimal bad sequences are necessary for a uniform Kruskal theorem
    Freund, A., Rathjen, M., Weiermann, A.
    Advances in Mathematics 400, article no. 108265, 44 pp (2022)
  • 1.
    R.E. Bruck, proof mining and a rate of asymptotic regularity for ergodic averages in Banach spaces
    Freund, A., Kohlenbach, U.
    Applied Set-Valued Analysis and Optimization 4, 323-336 (2022)
  • 1.
    A mathematical commitment without computational strength
    Freund, A.
    The Review of Symbolic Logic 15, 880-906 (2022)
  • 1.
    Boundedness theorems for flowers and sharps
    Aguilera, J. P., Freund, A., Rathjen, M., Weiermann, A.
    Proceedings of the American Mathematical Society 150, 3973-3988 (2022)
  • 1.
    Patterns of resemblance and Bachmann-Howard fixed points
    Freund, A.
    Selecta Mathematica 28, article no. 19, 32 pp (2021)
  • 1.
    Derivatives of normal functions in reverse mathematics
    Freund, A., Rathjen, M.
    Annals of Pure and Applied Logic 172, article no. 102890, 49 pp (2021)
  • 1.
    Ackermann and Goodstein go functorial
    Aguilera, J. P., Freund, A., Rathjen, M., Weiermann, A.
    Pacific Journal of Mathematics 313, 251-291 (2021)
  • 1.
    Well ordering principles and Pi^1_4-statements: a pilot study
    Freund, A.
    The Journal of Symbolic Logic 86, 709-745 (2021)
  • 1.
    Predicative collapsing principles
    Freund, A.
    The Journal of Symbolic Logic 85, 511-530 (2020)
  • 1.
    From Kruskal’s theorem to Friedman’s gap condition
    Freund, A.
    Mathematical Structures in Computer Science 30, 952-975 (2020)
  • 1.
    Set-theoretic reflection is equivalent to induction over well-founded classes
    Freund, A.
    Proceedings of the American Mathematical Society 148, 4503-4515 (2020)
  • 1.
    What is effective transfinite recursion in reverse mathematics?
    Freund, A.
    Mathematical Logic Quarterly 66, 479-483 (2020)
  • 1.
    Short Proofs for Slow Consistency
    Freund, A., Pakhomov, F.
    Notre Dame Journal of Formal Logic 61, 31-49 (2020)
  • 1.
    How strong are single fixed points of normal functions?
    Freund, A.
    The Journal of Symbolic Logic 85, 709-732 (2020)
  • 1.
    A note on ordinal exponentiation and derivatives of normal functions
    Freund, A.
    Mathematical Logic Quarterly 66, 326-335 (2020)
  • 1.
    A categorical construction of Bachmann-Howard fixed points
    Freund, A.
    Bulletin of the London Mathematical Society 51, 801-814 (2019)
  • 1.
    Computable aspects of the Bachmann-Howard principle
    Freund, A.
    Journal of Mathematical Logic 20, article no. 2050006, 26 pp (2019)
  • 1.
    Pi^1_1-comprehension as a well-ordering principle
    Freund, A.
    Advances in Mathematics 355, article no. 106767, 65 pp (2019)
  • 1.
    A note on iterated consistency and infinite proofs
    Freund, A.
    Archive for Mathematical Logic 58, 339-346 (2018)
  • 1.
    Proof lengths for instances of the Paris-Harrington principle
    Freund, A.
    Annals of Pure and Applied Logic 168, 1361-1382 (2017)
  • 1.
    Slow reflection
    Freund, A.
    Annals of Pure and Applied Logic 168, 2103-2128 (2017)
  • 1.
    Lattice-based and topological representations of binary relations with an application to music
    Andreatta, M., Freund, A., Giavitto, J.-L.
    Annals of Mathematics and Artificial Intelligence 73, 311-334 (2015)

  • 1.
    A Uniform Characterization of Sigma_1-Reflection over the Fragments of Peano Arithmetic
    Freund, A.
    In: Mainzer, K., Schuster, P., and Schwichtenberg, H. (eds.) Proof and Computation II. From Proof Theory and Univalent Mathematics to Program Extraction and Verification. pp. 189-253. World Scientific, Singapore (2022)

  • 1.
    Proof mining a nonlinear ergodic theorem for Banach spaces (abstract)
    Freund, A., Kohlenbach, U.
    Dagstuhl Report 11, 158-159 (2022)
  • 1.
    Goodstein’s theorem meets reverse mathematics (abstract)
    Aguilera, J. P., Freund, A., Rathjen, M., Weiermann, A.
    Oberwolfach Report 34, 1701-1703 (2020)
  • 1.
    Type‐Two Well‐Ordering Principles and Pi^1_1-Comprehension (abstract)
    Freund, A.
    The Bulletin of Symbolic Logic 24, 228 (2018)
  • 1.
    The slow reflection hierarchy (abstract)
    Freund, A.
    The Bulletin of Symbolic Logic 23, 240-241 (2017)
  • 1.
    Proof Length and the Paris‐Harrington Principle (abstract)
    Freund, A.
    Oberwolfach Report 14, 3129–3130 (2017)
  • 1.
    Where can we really prove instances of the Paris‐Harrington Principle? (abstract)
    Freund, A.
    Proceedings in Applied Mathematics and Mechanics 16, 903-904 (2016)