We describe Wadge degrees of $\omega$-languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ${\xi }^{\omega }$ where $\xi ={\omega }_1^{\mathrm{CK}}$ is the first non-recursive ordinal known as the Church–Kleene ordinal. This answers a question raised in [2].

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 [2].