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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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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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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