The complexity of quasivariety lattices of unary algebras

Abstract

The question of what is considered as the complexity of the lattice of quasivarieties and what lattices of quasivarieties are complex according to some degree of complexity, and which are not, has been studied by many authors. The paper considers two measures of complexity of lattices of quasivarieties. A study is made of the complexity of the lattice structure of quasivarieties of unary algebras. The relationship between two measures of the complexity of lattices of quasivarieties is studied.M.V. Schwiedefsky and A.Zamoyska-Jenio, the following problem was posed: is there a non-Q-universal class for which the set of all finite sublattices of the lattice of quasivarieties is not computable? The author has proved the non-trivial identity satisfying on the lattices of quasivarieties of unary algebras, as a result of which a certain result is obtained with respect to this problem.