Stone algebras form an equational class: (Remarks on Lattice Theory III)

On the Equational Theory of Representable Polyadic Equality Algebras

Among others we will see that the equational theory of ! dimensional rep-resentable polyadic equality algebras (RPEA ! 's) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is nite schema-axiomatizable (and hence the equational theory of this class is nite schema-axi...

Remarks on Topological Algebras

The article discusses some subjects of topological polylinear algebra closely related to the theory of chiral/vertex algebras. 2000 Math. Subj. Class. 14A22.

Equational Logic and Equational Theories of Algebras

Non-computability of the Equational Theory of Polyadic Algebras

In [3] Daigneault and Monk proved that the class of (ω dimensional) representable polyadic algebras (RPAω for short) is axiomatizable by finitely many equationschemas. However, this result does not imply that the equational theory of RPAω would be recursively enumerable; one simple reason is that the language of RPAω contains a continuum of operation symbols. Here we prove the following. Roughl...

Remarks on completeness of lattice-valued Cauchy spaces

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.