Strong density of definable types and closed ordered differential fields
Logic
2019-09-18 v3
Abstract
The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable subset X of M^n, there is a definable type p in X, definable over a code for X and of the same d-dimension as X. Both o-minimal theories and the theory of closed ordered differential fields (CODF) are shown to have this property. As an application, we derive a new proof of elimination of imaginaries for CODF.
Keywords
Cite
@article{arxiv.1704.08396,
title = {Strong density of definable types and closed ordered differential fields},
author = {Quentin Brouette and Pablo Cubides Kovacsics and Francoise Point},
journal= {arXiv preprint arXiv:1704.08396},
year = {2019}
}
Comments
There was a mistake page 3, spotted by Anand Pillay, on the canonical base of a type. (It did not affect the results of the paper.)