Varieties of two-dimensional cylindric algebras II

In [2] we investigated the lattice ⋀(Df₂) of all subvarieties of the variety Df₂ of two-dimensional diagonal free cylindric algebras. In the present paper we investigate the lattice ⋀(CA₂) of all subvarieties of the variety CA₂ of two-dimensional cylindric algebras. We prove that the cardinality of ⋀(CA₂) is that of the continuum, give a criterion for a subvariety of CA₂ to be locally finite, and describe the only pre locally nite subvariety of CA2. We also characterize nitely generated subvarieties of CA2 by describing all fteen pre nitely generated subvarieties of CA₂. Finally, we give a rough picture of ⋀(CA₂), and investigate algebraic properties preserved and reected by the reduct functors \( \mathbb{F}: \mathbf{CA}_2 and \Phi : \Lambda (\mathbf{CA}_2) \rightarrow (\Lambda (\mathbf{Df}_2) \).

Authors and Affiliations

1. Institute for Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

   Nick Bezhanishvili

Corresponding author

Correspondence to Nick Bezhanishvili.

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