Characteristic Sequence of Strongly Minimal Directed Single Graphs of 1-Arity

Abstract

In this paper, we will classify the strongly minimal directed single graphs of 1-arity by axiomatizing the theory of characteristic sequence of such a graph. Then we will show this theory is complete by using Łos-Vaught test. Complete theory is important to capture all the models of the theory and hence can be applied on mathematical structures which meet such a theory. The theory of algebraically closed fields with a given characteristic is complete. Thus, in this paper we will classify the strongly minimal directed single graphs of 1-arity with given characteristic sequence which can be applied on many mathematical structures not only algebraically closed fields.