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

Elliot Kaplan

Vol. 320 (2022), No. 2, 261–298
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.

Keywords
o-minimality, spherical completeness, valued differential fields
Mathematical Subject Classification
Primary: 03C64
Secondary: 12H05, 12J10
Milestones
Received: 21 April 2021
Revised: 27 July 2022
Accepted: 27 September 2022
Published: 15 February 2023
Authors
Elliot Kaplan
Department of Mathematics and Statistics
McMaster University
Hamilton, ON
Canada