It is shown how Lawvere's one-to-one translation between Birkhoff's description of varieties and the categorical one (see [6]) turns Hu's theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.
@article{119217, author = {Hans-Eberhard Porst}, title = {Hu's Primal Algebra Theorem revisited}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {41}, year = {2000}, pages = {855-859}, zbl = {1048.08003}, mrnumber = {1800177}, language = {en}, url = {http://dml.mathdoc.fr/item/119217} }
Porst, Hans-Eberhard. Hu's Primal Algebra Theorem revisited. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 855-859. http://gdmltest.u-ga.fr/item/119217/
Distributive Lattices, University of Missouri Press, Missouri, 1974. | MR 0373985 | Zbl 0321.06012
Handbook of Categorical Algebra Vol. 2, Cambridge University Press, Cambridge, 1994.
Dualities and equivalences for varieties of algebras, in A.P. Huhn and E.T. Schmidt, editors, `Contributions to Lattice Theory' (Proc. Conf. Szeged 1980), vol. 33 of Coll. Math. Soc. János Bolyai, North-Holland, 1983, pp.101-275. | MR 0724265 | Zbl 0532.08003
Stone duality for Primal Algebra Theory, Math. Z. 110 (1969), 180-198. (1969) | MR 0244130 | Zbl 0175.28903
On the topological duality for Primal Algebra Theory, Algebra Universalis 1 (1971), 152-154. (1971) | MR 0294218 | Zbl 0236.08005
Functorial semantics of algebraic theories, PhD thesis, Columbia University, 1963. | MR 0158921 | Zbl 1062.18004
An algebraic version of categorical equivalence for varieties and more general algebraic theories, in A. Ursini and P. Agliano, editors, `Logic and Algebra', vol. 180 of Lecture Notes in Pure and Appl. Mathematics, Marcel Dekker, 1996, pp.211-243. | MR 1404941
Equivalence for varieties in general and for Bool in particular, to appear in Algebra Universalis. | MR 1773936