LEAST ENUMERATIONS OF UNARY PARTIAL STRUCTURES

In the present paper we consider structures with unary partial functions and partial predicates, called unary structures. Unary structures does not contain equality and inequality among the predicates of the structure. The main result obtained here is a characterization of the unary structures which have least enumerations, called degrees of the structures. As a corollary it is obtained a characterization of the unary structures which admit eective enumerations. There are some interesting results concerning the spectrum and the so-called quasi-degree of such structures.