  We construct a distributive algebraic lattice D that is not isomorphic to the
congruence lattice of any lattice. This solves a long-standing open problem,
traditionally attributed to R. P. Dilworth, from the forties. The lattice D has
compact top element and aleph omega+1 compact elements. Our results extend to
all algebras possessing a polynomially definable structure of a
join-semilattice with a largest element.
