Trois couleurs: A new non-equational theory
Logic
2020-09-21 v3
Abstract
A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality is a strengthening of stability yet so far only two examples of non-equational stable theories are known. We construct non-equational -stable theories by a suitable colouring of the free pseudospace, based on Hrushovski and Srour's original example.
Cite
@article{arxiv.1905.08294,
title = {Trois couleurs: A new non-equational theory},
author = {Amador Martin-Pizarro and Martin Ziegler},
journal= {arXiv preprint arXiv:1905.08294},
year = {2020}
}
Comments
The first author conducted research partially supported by the program GeoMod AAPG2019 (ANR-DFG). Both authors were supported by the program MTM2017-86777-P