Characteristic Sequence of Strongly Minimal Directed Single Graphs of 1-Arity
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 h...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/10/12/220 |
| Summary: | 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. |
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| ISSN: | 2079-3197 |