Christoph Kesting

Christoph Kesting

PhD in Model Theory

Publications

On T-Convexity, Non-Pfaffianness and Differential Fields

Published in Macsphere, 2026

We study the model theoretic expansions of certain fields by valuations, derivations, and pfaffian chains. In particular, we show that o-minimal expansions of real fields, equipped with a T -convex valuation and a monomial group of representatives, are well behaved if and only if an exponential function is not definable. Similarly, we show that differential expansions of ´ez-fields by a generic derivation are the same as taking the differentially large expansion. Further, we show that these expansions preserve certain model theoretic tameness properties, including NTP2. Further, we study the field extensions of the real exponential field by a pfaffian chain (a set of solutions to a triangular system of order one differential equations) and show that a real restriction of the Klein j-function is not Rexp-definable, indicating that these extensions are insufficient for certain applications in number theory

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Generic derivations, differential largeness and NTP2

Published in arxiv preprint, 2025

Joint work with Elliot Kaplan. We compare Fornasiero and Terzo’s framework of generic derivations on algebraically bounded structures with León Sánchez and Tressl’s differentially large fields. We show in the case of a single derivation that genericity and differential largeness coincide for éz-fields, as introduced by Walsberg and Ye. We also show that an NTP2 algebraically bounded structure remains NTP2 after expanding by a generic derivation.

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Tameness Properties in Multiplicative Valued Difference Fields with Lift and Section

Published in arxiv preprint, 2024

We prove relative quantifier elimination for Pals multiplicative valued difference fields with an added lifting map of the residue field. Furthermore, we generalize a NIP transfer result for valued fields by Jahnke and Simon to NTP2 to show that said valued difference fields are NTP2 if and only if value group and residue field are.

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The Klein j-Function is not Pfaffian over the Real Exponential Field

Published in arxiv preprint, 2023

James Freitag showed that the Klein j-function is not paffian over the complex numbers. We expand on this result by showing that a restriction of the Klein j-function to the imaginary interval (0, i) is not pfaffian over the real field exponential field in the sense of Miller and Speissegger.

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A dichotomy for T-convex fields with a monomial group

Published in Mathematical Logic Quarterly , 2023

Joint work with Elliot Kaplan. We prove a dichotomy for o-minimal fields R, expanded by a T-convex valuation ring (where T is the theory of R) and a compatible monomial group. We show that if T is power bounded, then this expansion of R is model complete (assuming that T is), it has a distal theory, and the definable sets are geometrically tame. On the other hand, if R defines an exponential function, then the natural numbers are externally definable in our expansion, precluding any sort of model theoretic tameness.

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