Some results on diagonal-free two-dimensional cylindric algebras

Varieties Of Two-Dimensional Diagonal-Free Cylindric Algebras. Part I

A construction of cylindric and polyadic algebras from atomic relation algebras

Given a simple atomic relation algebra A and a finite n ≥ 3, we construct effectively an atomic n-dimensional polyadic equality-type algebra P such that for any subsignature L of the signature of P that contains the boolean operations and cylindrifications, the L-reduct of P is completely representable if and only if A is completely representable. If A is finite then so is P. It follows that th...

On the Representation Theory for Cylindric Algebras

The main purpose of this paper is to give some new sufficient conditions for the representability of infinite dimensional cylindric algebras. We also discuss certain problems and results in the representation theory reported on by Henkin and Tarski in [5]. In general we adopt the notation of [5]. § 1 contains some additional notation, the statement of a representation theorem of Henkin and Tars...

Varieties of Two-dimensional Cylindric Algebras. Part I: Diagonal-free Case

We investigate the lattice Λ(Df2) of all subvarieties of the variety Df2 of two-dimensional diagonal-free cylindric algebras. We prove that a Df2algebra is finitely representable iff it is finitely approximable, characterize finite projective Df2-algebras, and show that there are no non-trivial injectives and absolute retracts in Df2. We prove that every proper subvariety of Df2 is locally fini...

Varieties of two-dimensional cylindric algebras II

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, ...