Varieties of two-dimensional cylindric algebras II
نویسنده
چکیده
In [2] we investigated the lattice Λ(Df 2) of all subvarieties of the variety Df2 of two-dimensional diagonal free cylindric algebras. In the present paper we investigate the lattice Λ(CA2) of all subvarieties of the variety CA2 of two-dimensional cylindric algebras. We prove that the cardinality of Λ(CA2) is that of the continuum, give a criterion for a subvariety of CA2 to be locally finite, and describe the only pre locally finite subvariety of CA2. We also characterize finitely generated subvarieties of CA2 by describing all fifteen pre finitely generated subvarieties of CA2. Finally, we give a rough picture of Λ(CA2), and investigate algebraic properties preserved and reflected by the reduct functors F : CA2 → Df2 and Φ: Λ(CA2) → Λ(Df2).
منابع مشابه
Varieties of Two-dimensional Cylindric Algebras. Part Ii
In [2] we investigated the lattice Λ(Df2) of all subvarieties of the variety Df2 of two-dimensional diagonal free cylindric algebras. In the present paper we investigate the lattice Λ(CA2) of all subvarieties of the variety CA2 of two-dimensional cylindric algebras. We give a dual characterization of representable two-dimensional cylindric algebras, prove that the cardinality of Λ(CA2) is that ...
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