PP-2000-10: Varieties of Two-Dimensional Diagonal-Free Cylindric Algebras. Part I.

PP-2000-10: Bezhanishvili, Nick (2000) Varieties of Two-Dimensional Diagonal-Free Cylindric Algebras. Part I. [Report]

Preview	Text (Full Text (PDF)) PP-2000-10.text.pdf Download (276kB) | Preview
	Text (Full Text (PS)) PP-2000-10.text.ps.gz Download (288kB)
	Text (Abstract) PP-2000-10.abstract.txt Download (1kB)

Abstract

This is the first part of the whole work which will consist of two
parts and intends to obtain a clear picture of the lattice
$\Lambda({\bf Df}_2)$ of all subvarieties of the variety {\bf Df}$_2$
of the two-dimensional diagonal-free cylindric algebras. Here we show
that every proper subvariety of {\bf Df}$_2$ is locally finite, and
hence {\bf Df}$_2$ is hereditarily finitely approximable. Moreover, we
prove that there exist exactly six critical varieties in $\Lambda({\bf
Df}_2)$, and characterize finite subvarieties of {\bf Df}$_2$. It is
also shown that a variety ${\bf V}\in\Lambda({\bf Df}_2)$ is
representable by its square algebras iff either ${\bf V}={\bf Df}_2$
or {\bf V} is a finite variety, and give a necessary and sufficient
condition for a finite variety to be representable. Representable
varieties by their rectangular algebras are also described. The
complexity of $\Lambda({\bf Df}_2)$ will be investigated in Part II.

Keyword(s): Cylindric Algebra Theory

Item Type:	Report
Report Nr:	PP-2000-10
Series Name:	Prepublication (PP) Series
Year:	2000
Date Deposited:	12 Oct 2016 14:36
Last Modified:	12 Oct 2016 14:36
URI:	https://eprints.illc.uva.nl/id/eprint/37

Actions (login required)

View Item