Submission date: 22 May 2019

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

Mathematics Subject Classification: 03C45

Keywords and phrases: Model theory, Equationality

Full text arXiv 1905.08294: pdf, ps.