On generalisations of the notion of semirecursiveness

In addition to the classes of semirecursive, weakly semirecursive, semirecursively enumerable, and $\operatorname{wsr}^*$ sets, introduced by Jockusch, Kummer, and Stephan, we define the classes of almost and partially semirecursive sets and completely describe the relations between these classes with respect to inclusion.