**Gödel's completeness theorem**

The set of propositions provable in Predicate Logic has a Model Theory. In other words, the truth defined by Proof Theory and the truth defined by Model Theory coincide which means If a proposition is provable in a logical system, then that proposition is true in all models of that system.

This theorem does not contradict Gödel’s incompleteness theorem but is not satisfied in Higher-order logics.