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

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.

arXiv comment26 pages

References in corpus (4)

• Some properties of analytic difference fields
• Generic derivations on o-minimal structures
• Maximal immediate extensions of valued differential fields
• Differential-henselianity and maximality of asymptotic valued differential fields

Cited by in corpus (2)

• Spherically complete models of Hensel minimal valued fields
• Monotone $T$-convex $T$-differential fields