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.
Предметные области OECD FOS+WOS
- 1.01 МАТЕМАТИКА