On nonaxiomatizability of critical lattices class

O. E. Perminova

Ural Federal University named after First President of Russia B. N. Yeltsin, 19, Mira Street, Ekaterinburg, 620002

Abstract: Rigid lattices, i.e., lattices, any its endomorphism is a constant endomorphism (mapping all elements to a some single element) or the identity endomorphism, are investigated. It is proved that the class of critical lattices is not axiomatizable.

Keywords: lattice, endomorphism, rigid lattice, critical lattice, axiomatizability.

UDC: 512.562