$T$convex $T$differential fields and their immediate extensions
Abstract
Let $T$ be a polynomially bounded ominimal 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 DOI:
 10.48550/arXiv.2104.10802
 arXiv:
 arXiv:2104.10802
 Bibcode:
 2021arXiv210410802K
 Keywords:

 Mathematics  Logic;
 Primary 03C64;
 Secondary 12H05;
 12J10
 EPrint:
 26 pages