This article is cited in 9 papers

Lattices of subclasses

M. V. Semenova^ab, A. Zamojska-Dzienio<sup>c

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Novosibirsk
^c Warsaw University of Technology, Warsaw, Poland

Abstract: We investigate the structure of lattices of subclasses of different types; among those are relative sub(quasi)variety lattices as well as relative (finitary) subprevariety lattices. Among other results, we prove a reduction theorem for (finitary) subprevariety lattices which generalizes a result of V. A. Gorbunov. We also answer a question by D. E. Palchunov and provide some noncomputability properties of lattices of relative subclasses.

Keywords: axiomatizable class, variety, quasivariety, prevariety, identity, quasi-identity, latticeю.

UDC: 512.56+512.57+510.53

Received: 02.04.2011

 English version: Siberian Mathematical Journal, 2012, 53:5, 889–905

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