DEFINABILITY OF JUMP CLASSES IN THE LOCAL THEORY OF THE $ω$-ENUMERATION DEGREES (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2015)
In the present paper we continue the study of the definability in the local substructure $\mathcal{G}$ of the $ω$-enumeration degrees, which was started in the work of Ganchev and Soskova [3]. We show that the class $I$ of the intermediate degrees is definable in $\mathcal{G}_ω$. As a consequence of our observations, we show that the first jump of the least $ω$-enumeration degree is also definable.