The ultrafilter number and hm

The cardinal invariant hm is defined as the minimum size of a family of c(min)-monochromatic sets that cover 2(omega) (where c(min)(x, y) is the parity of the biggest initial segment both x and y have in common). We prove that hm = omega(1) holds in Shelah's model of i < u, so the inequality hm < u is consistent with the axioms of ZFC. This answers a question of Thilo Weinert. We prove that the diamond principle lozenge(d) also holds in that model.