  We prove that if ZF is consistent then ZFC+GCH is consistent with the
following statement: There is for every k<omega a model of cardinality aleph_1
which is L_{infty,omega_1}-equivalent to exactly k non-isomorphic models of
cardinality aleph_1. In order to get this result we introduce ladder systems
and colourings different from the ``standard'' counterparts, and prove the
following purely combinatorial result: For each prime number p and positive
integer m it is consistent with ZFC+GCH that there is a ``good'' ladder system
having exactly p^m pairwise nonequivalent colourings.
