Antichain cutsets in real-ranked lattices

Abstract: We show that in a rank supersolvable lattice that is graded by a bounded real interval, any antichain cutset is a level set for some appropriately constructed grading. As a consequence, given an antichain cutset in any of the measurable Boolean lattice, a continuous partition lattice, or a continuous projective geometry, we may find a grading in which the cutset is a level set.