  We give in this paper additional answers to questions of Lescow and Thomas
[Logical Specifications of Infinite Computations, In:"A Decade of Concurrency",
Springer LNCS 803 (1994), 583-621], proving new topological properties of omega
context free languages : there exist some omega-CFL which are non Borel sets.
And one cannot decide whether an omega-CFL is a Borel set. We give also an
answer to questions of Niwinski and Simonnet about omega powers of finitary
languages, giving an example of a finitary context free language L such that
L^omega is not a Borel set. Then we prove some recursive analogues to preceding
properties: in particular one cannot decide whether an omega-CFL is an
arithmetical set.
