Nikolaos GALATOS , Jeffrey S . OLSON and James G . RAFTERY IRREDUCIBLE

A b s t r a c t. This paper deals with axiomatization problems for varieties of residuated meet semilattice-ordered monoids (RSs). An internal characterization of the finitely subdirectly irreducible RSs is proved, and it is used to investigate the varieties of RSs within which the finitely based subvarieties are closed under finite joins. It is shown that a variety has this closure property if its finitely subdirectly irreducible members form an elementary class. A syntactic characterization of this hypothesis is proved, and examples are discussed.