Congruence Lattice Problem - Semilattice Formulation of CLP

Semilattice Formulation of CLP

The congruence lattice Con A of an algebra A is an algebraic lattice. The (∨,0)-semilattice of compact elements of Con A is denoted by Conc A, and it is sometimes called the congruence semilattice of A. Then Con A is isomorphic to the ideal lattice of Conc A. By using the classical equivalence between the category of all (∨,0)-semilattices and the category of all algebraic lattices (with suitable definitions of morphisms), as it is outlined here, we obtain the following semilattice-theoretical formulation of CLP.

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Famous quotes containing the word formulation:

    In necessary things, unity; in disputed things, liberty; in all things, charity.
    —Variously Ascribed.

    The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)