Infinite intervals in free lattices

摘要

ifu/vis any infinite interval in FL(X), the free lattice with generating setX, and$${text{Y}} leqslant {text{X}} + aleph _0 $$thenu/vcontains a sublattice isomorphic to FL(Y). This result answers a question posed by Ralph Freese and J. B. Nation in their paper “Covers in Free Lattices” 2 and the principal techniques used in proving this result all come from that paper. The most difficult step in the argument is to show that there are incomparable elements in any infinite inter