Wadge degrees of ω-languages of deterministic turing machines

Abstract

We describe Wadge degrees of ω-languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξω where ξ = ω1CK is the first non-recursive ordinal known as the Church-Kleene ordinal. This answers a question raised in [Du0?]. © Springer-Verlag Berlin Heidelberg 2003.