A selfdual embedding of the free lattice over countably many generators into the three-generated one

摘要

By a 1941 result of Whitman, the free lattice FL(3) = FL(x, y, z) includes a sublattice FL(omega) freely generated by infinitely many elements. Let delta denote the unique dual automorphism of FL(x, y, z) that acts identically on the set {x, y, z} of generators. We prove that FL(x, y, z) has a sublattice S isomorphic to FL(omega) such that delta(S) = S.