Positive Sugihara monoids

It is proved that in the variety of positive Sugihara monoids, every finite subdirectly irreducible algebra is a retract of a free algebra. It follows that every quasivariety of positive Sugihara monoids is a variety, in contrast with the situation in several neighboring varieties. This result shows that when the logic R-mingle is formulated with the Ackermann constant t, then its full negation-free fragment is hereditarily structurally complete. Presented by R. W. Quackenbush. Received August 28, 2005; accepted in final form July 31, 2006.