  Let P be a distinguished unary predicate and
  K= {M: M a model of cardinality aleph_n with P^M of cardinality aleph_0}.
  We prove that consistently for n=4, for some countable first order theory T
we have: T has no model in K whereas every finite subset of T has a model in K.
We then show how we prove it also for n=2, too.
