Vaught's test

For the result characterizing elementary substructures, see Tarski-Vaught test.

In mathematical logic, Vaught's test is a sufficient condition for the completeness of a set of sentences in a first order language. Let $Γ$ be such a set, in a language $\mathfrak L$ with no finite models and assume it is $κ$ -categorical for some $\kappa \ge \mathfrak |L|$ . Then $Γ$ is complete.