REMARKS ON CATEGORIES OF ALGEBRAS DEFINED BY A PROPER CLASS OF OPERATIONS
Horst Herrlich · Quaestiones Mathematicae · 1990
A category A of algebras is constructed, which has the following features: A is an HSP-class of algebras. A is not equationally definable. A is implicationally definable. However an illegitimate collection of implications, each having a proper class of premises, is needed.