Generalised power series determined by linear recurrence relations (with Salma Kuhlmann and Michele Serra), J. Algebra 681 (2025) 152–189, doi:10.1016/j.jalgebra.2025.05.012.
Ordered transexponential fields (with Salma Kuhlmann), Ann. Pure Appl. Logic 176 (2025) Article 103541, 23 pages, doi:10.1016/j.apal.2024.103541.
A Simple Explanation for Harmonic Word Order (John Mansfield and K.), Cognitive Sci. 49 (2025) Article e70056, 31 pages, doi:10.1111/cogs.70056.
Embedding the prime model of real exponentiation into o-minimal exponential fields, Bull. Lond. Math. Soc. 56 (2024) 907–913, doi:10.1112/blms.12972. – Review MR4730752, Zbl 07815307.
Bildung mit und über KI in der Schule: Umsetzung einer partizipativen Unterrichtsplattform (as contributor of KI macht Schule Team, with S. Schönbrodt, H. Dohmen, P. Pommer, S. Schneider and N. Berberich), Proceedings of DELFI Workshops 2024 (eds N. Kiesler and S. Schulz; Gesellschaft für Informatik e.V., Bonn, 2024) 157–164, doi:10.18420/delfi2024-ws-21.
Definable valuations on ordered fields (with Philip Dittmann, Franziska Jahnke and Salma Kuhlmann), Model Theory 2 (2023) 101–120, doi:10.2140/mt.2023.2.101. — Review MR4659507, Zbl 1532.13002.
Definability of henselian valuations by conditions on the value group (with Salma Kuhlmann and Moritz Link), J. Symb. Log. 88 (2023) 1064–1082, doi:10.1017/jsl.2022.34. — Review MR4636625, Zbl 07735945.
On Rayner structures (with Salma Kuhlmann and Michele Serra), Comm. Algebra 50 (2022) 940–948, doi:10.1080/00927872.2021.1976789. — Review MR4379648, Zbl 1483.13039.
Strongly NIP almost real closed fields (with Salma Kuhlmann and Gabriel Lehéricy), Math. Log. Q. 67 (2021) 321–328, doi:10.1002/malq.202000060. — Review MR4370208, Zbl 1521.03071.
Ordered fields dense in their real closure and definable convex valuations (with Salma Kuhlmann and Gabriel Lehéricy), Forum Math. 33 (2021) 953–972, doi:10.1515/forum-2020-0030. — Review MR4279111, Zbl 1521.12009.
Models of true arithmetic are integer parts of models of real exponentiation (with Merlin Carl), J. Log. Anal. 13:3 (2021) 21 pages, doi:10.4115/jla.2021.13.3. — Review MR4257176, Zbl 1493.03005.
Value groups and residue fields of models of real exponentiation, J. Log. Anal. 11:1 (2019) 23 pages, doi:10.4115/jla.2019.11.1. — Review MR3978729, Zbl 1459.13015.
Education with and about AI: Implementation of a participatory teaching platform (Extended Abstract; as contributor of KI macht Schule Team, with S. Schönbrodt, S. Schneider and N. Berberich), Proceedings of the Symposium on Integrating AI and Data Science into School Education Across Disciplines 2025.
Algebraic and Model Theoretic Properties of O-minimal Exponential Fields (Thesis Abstract), Bull. Symb. Log. 27 (2021) 529–530, doi:10.1017/bsl.2021.64. — MR4386796.
Ordered Fields Dense in Their Real Closure and Definable Convex Valuations (with Salma Kuhlmann and Gabriel Lehéricy), Proceedings of the Séminaire de Structures Algébriques Ordonnées 2018–2020.
Strongly NIP Almost Real Closed Fields (with Salma Kuhlmann and Gabriel Lehéricy), Proceedings of the Séminaire de Structures Algébriques Ordonnées 2018–2020.
On Strongly NIP Ordered Fields and Definable Convex Valuations (with Salma Kuhlmann and Gabriel Lehéricy, not intended for further publication), 2019, arXiv:1810.10377.
O-minimal exponential fields and their residue fields (Extended Abstract), Oberwolfach Rep. 13 (2016) 3357–3359, doi:10.4171/OWR/2016/60. — MR3757068, Zbl 1390.00071.
Insights into the mind using tools from Explainable AI: A practical introduction to SHAP in cognitive science (Guido M. Linders, K. and Stefan Schnell), 2025, PsyArXiv, doi:10.31234/osf.io/v4krw_v1.
On Tameness, Measurability and the Independence Property (with Matthieu Vermeil and Laura Wirth), 2025, arXiv:2506.08733.
Measurability in the Fundamental Theorem of Statistical Learning (with Laura Wirth), 2025, arXiv:2410.10243.
Definable ranks (with Lasse Vogel and Salma Kuhlmann), 2025, arXiv:2506.00443.
Definable henselian valuations on dp-minimal real fields (with Lasse Vogel and Salma Kuhlmann), 2024, arXiv:2410.10344.
Automorphisms and derivations on algebras endowed with formal infinite sums (with Vincent Bagayoko, Salma Kuhlmann, Michele Serra and Daniel Panazzolo), 2024, arXiv:2403.05827.
Mathematical theory of exact SHAP values (K., Guido M. Linders and Stefan Schnell); in: G. M. Linders, L. S. Krapp, S. Schnell, Insights into the mind using tools from Explainable AI: A practical introduction to SHAP in cognitive science, osf.io/rvawk.
A formal mathematical description of frequency-based harmonic word order (K. and John Mansfield); in: J. Mansfield, Harmonic word order, osf.io/m94en, doi:10.13140/RG.2.2.28028.86408; to: A simple explanation for harmonic word order (John Mansfield und K.), Cognitive Sci. 49 (2025) Article e70056, 31 pages, doi:10.1111/cogs.70056.
Ordered Algebraic Structures: Hahn Fields, Convex Valuations, and Exponentials (October 2023)
published in KOPS, urn:nbn:de:bsz:352-2-1ljrlhqax4j190
Mentor: Prof. Salma Kuhlmann
Referees: MCF Dr Mickaël Matusinski, Prof. Tobias Kaiser, Prof. Immanuel Halupczok
Habilitation commission: Prof. Salma Kuhlmann (chair), Prof. Jochen Glöckner, Prof. Sven Kosub, Prof. Stephan Schumann and all professors of the Dapartment of Mathematics and Statistics of the University of Konstanz (see Habilitation regulations)
University of Konstanz
Further material: Habilitation talk Künstliche neuronale Netze und Vapnik–Chervonenkis-Dimensionen (Announcement)
Habilitation thesis will be shared upon request
Dissertation
Algebraic and Model Theoretic Properties of O-minimal Exponential Fields (July 2019)
published in KOPS, urn:nbn:de:bsz:352-2-166bghaubh8tf9
Supervisor and first referee: Prof. Salma Kuhlmann
Second referee: Prof. Tobias Kaiser
Doctoral committee: Prof. Claus Scheiderer (chair), Prof. Salma Kuhlmann, Prof. Tobias Kaiser
Further material: report on the significant foundation, contents and results, colloquium presentation
Masterarbeit
Schanuel's Conjecture and Exponential Fields (March 2015)
Betreuer: Prof. Dr. Jonathan Pila
University of Oxford
Weiteres: Aktualisierte Version, Résumé
Bachelorarbeit
Constructions of the real numbers – a set theoretical approach (March 2014)
Betreuer: Dr. Peter M. Neumann, DSc
University of Oxford
Weiteres: Aktualisierte Version, Präsentation
Growth of log-analytic functions (Tobias Kaiser, 2023), Mathematical Reviews, MR4598543.
The classification of dp-minimal and dp-small fields (Will Johnson, 2023), zbMATH, Zbl 1526.03003.
The étale open topology over the fraction field of a Henselian local domain (Will Johnson, Erik Walsberg and Jinhe Ye, 2023), zbMATH, Zbl 07747092.
On a differential intermediate value property (Matthias Aschenbrenner, Lou van den Dries and Joris van der Hoeven, 2022), Mathematical Reviews, MR4477287.
Henselian discrete valued stable fields (Ivan Chipchakov, 2022), Mathematical Reviews, MR4453883.
Interpretable fields in various valued fields (Yatir Halevi, Assaf Hasson and Ya’acov Peterzil, 2022), Mathematical Reviews, MR4413217.
Logarithms, constructible functions and integration on non-archimedean models of the theory of the real field with restricted analytic functions with value group of finite archimedean rank (Tobias Kaiser, 2022), Mathematical Reviews, MR4358456.
On the non-uniqueness of maximal purely wild extensions (Arpan Dutta, 2022), zbMATH, Zbl 1492.12005.
The domination monoid in o-minimal theories (Rosario Mennuni, 2022), zbMATH, Zbl 1509.03105.
On the value group of the transseries (Alessandro Berarducci and Pietro Freni, 2021), Mathematical Reviews, MR4305776.
Surreal ordered exponential fields (Philip Ehrlich and Elliot Kaplan, 2021), zbMATH, Zbl 1495.03057.
Extending valuations to the field of rational functions using pseudo-monotone sequences (Giulio Peruginelli and Dario Spirito, 2021), zbMATH, Zbl 1482.12007.
Surreal ordered exponential fields (Philip Ehrlich and Elliot Kaplan, 2021), zbMATH, Zbl 1495.03057.
Herr Dr. Krapp, sagt KI die Wahrheit?, Singener Wochenblatt, 27 November 2024, p. 31, in German. – Link to online article.
Wahr oder falsch? Ein Algorithmus entscheidet..., Mitt. Dtsch. Math.-Ver. 29 (2021) 151–152, doi:10.1515/dmvm-2021-0057. — MR4323381.
Wahr oder falsch?, KlarText 2021 (Klaus Tschira Stiftung; TEMPUS Corporate, ZEIT, 2021) 30–33.
I am mainly interested in the model theoretic study of ordered algebraic structures. This involves the topics of o-minimality, non-archimedean fields, generalised power series, ordered exponential fields (in particular, the real exponential field), integer parts, models of Peano Arithmetic, definable valuations, ordered abelian groups and the surreal numbers. Many of the questions motivating my work originate from Mathematical Logic and have connections to Valuation Theory, Real Algebra, Set Theory, Real Analysis, Group Theory and Recursion Theory.
August to September 2023: McMaster University, as guest of Dr Elliot Kaplan in the Ontario/Baden-Württemberg Faculty Mobility Programme; one month
August to September 2022: Mathematik Munster: Dynamik – Geometrie – Struktur, University of Münster, as guest of Professor Franziska Jahnke; three weeks
May to June 2022: The Fields Institute, University of Toronto, Thematic Program on Tame Geometry, Transseries and Applications to Analysis and Geometry; four weeks as Long Term Visitor
March 2018: Institut Henri Poincaré, Sorbonne Université, Model Theory, Combinatorics and Valued Fields; one month
April 2016: Mathematical Institute, University of Münster, Model Theory Month in Münster; two weeks
November 2014 to January 2015: Department of Mathematical Logic, Mathematical Institute of the University of Freiburg, as guest of Professor Heike Mildenberger; acht Wochen
September 2014: Arbeitsgruppe: Wissenschaftliches Rechnen im Exascale Zeitalter, Sommerakademie Krakau, Studienstiftung des deutschen Volkes, Lead by: Professor Dominik Göddeke, Assistant Professor Matthias Möller; zwei Wochen