Trois couleurs: A new non-equational theory

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 $\omega$-stable theories by a suitable colouring of the free pseudospace, based on Hrushovski and Srour's original example.

The first author conducted research partially supported by the program GeoMod AAPG2019 (ANR-DFG). Both authors were supported by the program MTM2017-86777-P