  A numbering of a countable family $S$ is a surjective map from the set of
natural numbers $\omega$ onto $S$. A numbering $\nu$ is reducible to a
numbering $\mu$ if there is an effective procedure which given a $\nu$-index of
an object from $S$, computes a $\mu$-index for the same object. The
reducibility between numberings gives rise to a class of upper semilattices,
which are usually called Rogers semilattices. The paper studies Rogers
semilattices for families $S \subset P(\omega)$ belonging to various levels of
the analytical hierarchy. We prove that for any non-zero natural numbers $m\neq
n$, any non-trivial Rogers semilattice of a $\Pi^1_m$-computable family cannot
be isomorphic to a Rogers semilattice of a $\Pi^1_n$-computable family. One of
the key ingredients of the proof is an application of the result by Downey and
Knight on degree spectra of linear orders.
