(untitled) (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 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 G_ω. As a consequence of our observations, we show that the first jump of the least ω-enumeration degree is also definable.