DEFINABILITY OF JUMP CLASSES IN THE LOCAL THEORY OF THE $\omega$-ENUMERATION DEGREES

In the present paper we continue the study of the definability in the local substructure $\mathcal{G}$ of the $\omega$-enumeration degrees, which was started in the work of Ganchev and Soskova [3]. We show that the class $\textbf{I}$ of the intermediate degrees is definable in $\mathcal{G}_\omega$. As a consequence of our observations, we show that the first jump of the least $\omega$-enumeration degree is also definable.