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29 Jun 1990


      I haven't had a chance yet to follow up on Mike Barr's thoughts, but
hopefully will when I get back from the Jonsson symposium.  Meanwhile
here's a message from Pepe Meseguer giving some key references, which
would appear to be prerequisite reading for anyone formulating ideas
in this area.
-v

        All of this has been done for ordered algebras by Steve Bloom,
        who defined ordered theories and proved a Birkhoff variety
        theorem in "Varieties of ordered algebras" JCSS 13 (1976)
        200-212, and for (chain) continuous ordered algebras by me, who
        used continuous theories, and proved a completeness theorem and
        two different Birkhoff variety theorems in "Varieties of
        Chain-Complete Algebras" J. Pure Appl. Algebra, 19 (1980)
        347-383, and in "A Birkhoff-like theorem for algebraic clases
        of interpretations of program schemes" in "Formalization of
        Programming Concepts" J. Diaz and I. Ramos (eds.) Springer LNCS
        107, (1981) 151-168.

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Vaughan Pratt