Submission date: 28 February 2020

Abstract:

Let (R, δ) be a closed ordered differential field, and C its field of constants. In this note, we prove that for sets definable in the pair (R, C), the δ-dimension and the large dimension coincide. As an application, we characterize the definable sets that are internal to C, as those sets that are definable in (R, C) and have δ-dimension 0. We further show that having δ-dimension 0 does not generally imply co-analyzability in C.

Mathematics Subject Classification: 03C98, 03C60

Keywords and phrases: Closed ordered differential fields, dense pairs of o-minimal structures, differential and large dimension

Full text arXiv 2002.12929: pdf, ps.