Trois couleurs: A new non-equational theory
Volume 254 / 2021
Fundamenta Mathematicae 254 (2021), 313-333
MSC: Primary 03C45.
DOI: 10.4064/fm953-9-2020
Published online: 11 February 2021
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.
