Some complete $\omega$-powers of a one-counter language in the difference hierarchy

Jacques Duparc, Olivier Finkel, Dominique Lecomte

Fix a finite alphabet $\Sigma$ having at least two letters, and natural numbers $n,k\ge 1$. We denote by $D_n({\mathbf{\Pi }}_k^0)$ the class of differences of $n$ subsets of the Cantor space…