Schmidt's Approach Via Distributive Join-homomorphisms
We say that a (∨,0)-semilattice satisfies Schmidt's Condition, if it is isomorphic to the quotient of a generalized Boolean semilattice B under some distributive join-congruence of B. One of the deepest results about representability of (∨,0)-semilattices is the following.
Theorem (Schmidt 1968). Any (∨,0)-semilattice satisfying Schmidt's Condition is representable.
This raised the following problem, stated in the same paper.
Read more about this topic: Congruence Lattice Problem
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