We study the structure of algebraic
-closed subsets of an algebraic lattice
L, where
is some Browerian binary relation on
L, in the special case when the lattice of such subsets is an atomistic lattice. This gives an approach to investigate the atomistic lattices of congruence-Noetherian quasivarieties.
Keywords Lattice - quasivariety - quasi-order - algebraic subsets
V. A. Gorbunov has died in January 1999
Special issue of Studia Logica: 
Algebraic Theory of Quasivarieties
Presented by
M. E. Adams, W. Dziobiak, and A. V. Kravchenko