 Gödel's completeness theorem

For first-order logic, every sentence true in every model of a theory is derivable from that theory. Equivalently, every consistent theory has a model.

Gödel's Completeness Theorem is a fundamental result in mathematical logic, formulated by Kurt Gödel in 1929. The theorem states that every consistent formal system of first-order logic has a model, meaning that if a set of sentences in first-order logic is consistent (i.e., it does not derive a contradiction), then there exists an interpretation under which all the sentences in that set are true.