Reports on Mathematical Logic

No. 43

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

Irreducible Residuated Semilattices and Finitely Based Varieties

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.

Department of Mathematics, University of Denver, 2360 S. Gaylord St., Denver, CO 80208, USA

Department of Mathematics, Norwich University, 158 Harmon Dr., Northfield, VT, 05663, USA

School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000 South Africa

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