The universal Lachlan semilattice without the greatest element

We deal with some upper semilattices of $m$-degrees and of numberings of finite families. It is proved that the semilattice of all c.e. $m$-degrees, from which the greatest element is removed, is isomorphic to the semilattice of simple $m$-degrees, the semilattice of hypersimple $m$-degrees, and the semilattice of $\Sigma_2^0$-computable numberings of a finite family of $\Sigma_2^0$-sets, which contains more than one element and does not contain elements that are comparable w.r.t. inclusion.