Some of my research interests are listed below. More information about my publications, talks and teaching can be accessed via the menu at the top of this page.
Email: freund AT mathematik DOT tu-darmstadt DOT de
- A streamlined presentation of the main result from my thesis is available via arXiv:1809.06759. I have also written two papers which complement and improve the main result (containing material from my thesis as well as new material). They are available via arXiv:1809.06769 and arXiv:1809.06774.
- My PhD thesis Type-Two Well-Ordering Principles, Admissible Sets, and Π11-Comprehension is now available via White Rose eTheses Online.
- My paper A Note on Iterated Consistency and Infinite Proofs has been accepted for publication in the Archive for Mathematical Logic. A free view-only version can be accessed via Springer Nature's SharedIt.
- A video of my talk at the Hausdorff Trimester Program Types, Sets and Constructions is available on YouTube.
- 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