Pro-definability of spaces of definable types
Abstract
We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, -adically closed fields, real closed and algebraically closed valued fields and closed ordered differential fields. Furthermore, we prove pro-definability of other distinguished subspaces, some of which have an interesting geometric interpretation. Our general strategy consists in showing that definable types are uniformly definable, a property which implies pro-definability using an argument due to E. Hrushovski and F. Loeser. Uniform definability of definable types is finally achieved by studying classes of stably embedded pairs.
Keywords
Cite
@article{arxiv.1905.11059,
title = {Pro-definability of spaces of definable types},
author = {Pablo Cubides Kovacsics and Jinhe Ye},
journal= {arXiv preprint arXiv:1905.11059},
year = {2022}
}
Comments
We divide the original article into two parts. The current update contains the work about uniform definability and pro-definability in different theories. The part concerning strict pro-definability and axiomatization of tame pairs will be updated separately