It was first proved by Birkhoff and Frink, and the result now belongs to the folklore, that any algebraic lattice is up to isomorphism the lattice of subuniverses of a universal algebra. A study of subsystems of a transition system yields a new algebraic concept, that of a strongly algebraic lattice. We give here a representation theorem to the manner of Birkhoff and Frink of such lattices.
S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, vol. 78 of Graduate Texts in Mathematics, Springer, New York, 1981.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC. Centazzo, J. Rosický, and E. M. Vitale, “A characterization of locally -presentable categories,” Cahiers de Topologie et Géométrie Différentielle Catégoriques, vol. 45, no. 2, pp. 141–146, 2004.
View at: Google Scholar | Zentralblatt MATH | MathSciNet