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Lawvere theory; equivalence between varieties; Hu's theorem; primal algebra; Post algebras
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.
[1] Balbes R., Dwinger Ph.: Distributive Lattices. University of Missouri Press, Missouri, 1974. MR 0373985 | Zbl 0321.06012
[2] Borceux F.: Handbook of Categorical Algebra Vol. 2. Cambridge University Press, Cambridge, 1994.
[3] Davey B.A., Werner H.: 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
[4] Hu T.K.: Stone duality for Primal Algebra Theory. Math. Z. 110 (1969), 180-198. MR 0244130 | Zbl 0175.28903
[5] Hu T.K.: On the topological duality for Primal Algebra Theory. Algebra Universalis 1 (1971), 152-154. MR 0294218 | Zbl 0236.08005
[6] Lawvere F.W.: Functorial semantics of algebraic theories. PhD thesis, Columbia University, 1963. MR 0158921 | Zbl 1062.18004
[7] McKenzie R.: 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
[8] Porst H.-E.: Equivalence for varieties in general and for Bool in particular. to appear in Algebra Universalis. MR 1773936
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