Wadge Hierarchy of Omega Context Free Languages

The main result of this paper is that the length of the Wadge hierarchy of omega context free languages is greater than the Cantor ordinal epsilon_0, and the same result holds for the conciliating Wadge hierarchy, defined by J. Duparc, of infinitary context free languages, studied by D. Beauquier. In the course of our proof, we get results on the Wadge hierarchy of iterated counter omega languages, which we define as an extension to omega languages of classical (finitary) iterated counter languages