PP200218: Bezhanishvili, Nick (2002) Varieties of TwoDimensional Cylindric Algebras. Part II. [Report]
Preview 
Text (Full Text (PDF))
PP200218.text.pdf Download (267kB)  Preview 
Text (Full Text (PS))
PP200218.text.ps.gz Download (263kB) 

Text (Abstract)
PP200218.abstract.txt Download (1kB) 
Abstract
In the precursor to this report, we investigated the lattice
$\Lambda(Df_2)$ of all subvarieties of the variety $Df_2$ of
twodimensional diagonal free cylindric algebras. In the present paper
we investigate the lattice $\Lambda(CA_2)$ of all subvarieties of the
variety $CA_2$ of twodimensional cylindric algebras. We give a dual
characterization of representable twodimensional cylindric algebras,
prove that the cardinality of $\Lambda(CA_2)$ is that of continuum,
give a criterion for a subvariety of $CA_2$ to be locally finite, and
describe the only pre locally finite subvariety of $CA_2$. We also
characterize finitely generated subvarieties of $CA_2$ by describing
all fifteen pre finitely generated subvarieties of $CA_2$. Finally, we
give a rough picture of $\Lambda(CA_2)$, and investigate algebraic
properties preserved and reflected by the reduct functors
$F : CA_2 \to Df_2$ and $\Phi : \Lamda(CA_2) \to \Lambda(Df2)$.
Item Type:  Report 

Report Nr:  PP200218 
Series Name:  Prepublication (PP) Series 
Year:  2002 
Date Deposited:  12 Oct 2016 14:36 
Last Modified:  12 Oct 2016 14:36 
URI:  https://eprints.illc.uva.nl/id/eprint/82 
Actions (login required)
View Item 