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arXiv · 2104.10802

$T$-convex $T$-differential fields and their immediate extensions

Elliot Kaplan
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Abstract

Let $T$ be a polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let $K$ be a model of $T$ equipped with a $T$-convex valuation ring and a $T$-derivation. If this derivation is continuous with respect to the valuation topology, then we call $K$ a $T$-convex $T$-differential field. We show that every $T$-convex $T$-differential field has an immediate strict $T$-convex $T$-differential field extension which is spherically complete. In some important cases, the assumption of polynomial boundedness can be relaxed to power boundedness.

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Elliot Kaplan. 2021-04-22. $T$-convex $T$-differential fields and their immediate extensions. https://doi.org/10.2140/pjm.2022.320.261

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