Continuous Algebras Revisited

摘要

For finitary Z-continuous algebras (where Z is a subset system), the Birkhoff Variety Theorem is proved in a new way, by means of the logic of inequalities. For infinitary separately Δ-continuous algebras, a counterexample is presented ( i.e., an HSP-class which is not a variety). In the logic of jointly Z-continuous algebras, tautologies are proved to be independent of Z, which provides a simple argument for the existence of absolutely free jointly Z-continuous algebras.