The finite lattice representation problem asks whether every finite lattice is isomorphic to the full congruence lattice of some finite algebra in universal algebra. Here the carrier is a nonempty set, and the signature is a finite list of operations of finite arity. Both the carrier size and the signature may depend on the lattice. A representation as a sublattice of a congruence lattice does not answer this question.
Finite Lattice Representation Problem
See also
Congruence Lattice, Lattice, Undecidable, Universal AlgebraExplore with Wolfram|Alpha
References
Burris, S. and Sankappanavar, H. P. A Course in Universal Algebra. New York: Springer-Verlag, 1981. https://math.uwaterloo.ca/~snburris/htdocs/ualg.html.Cite this as:
Weisstein, Eric W. "Finite Lattice Representation Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FiniteLatticeRepresentationProblem.html