Lattices in generative classes

Abstract

We define and study lattices in generative classes associated with generic structures. It is shown that these lattices can be non-distributive and, moreover, arbitrary enough. Heights and wights of the lattices are described. A model-theoretic criterion for the linear ordering is proved and these linear orders are described. Boolean algebras generated by the considered lattices are also described. © 2019 Kiouvrekis Y., Stefaneas P., Sudoplatov S.V.