Order-polynomially complete lattices

A lattice $(L, \vee, \wedge)$ is called ``order-plynomially complete'' (opc) if every monotone function from $L^n$ to $L$ is represented by a lattice-theoretic polynomial. The question whether infinite opc lattices can exist is open. It is known that the cardinality of such a lattice must be an inaccessible cardinal. We discuss some problems and results related to this problem.