 Kripke argues that the Church-Turing thesis is a corollary of Gödel’s completeness theorem for first-order predicate calculus with identity. Put somewhat crudely, the latter theorem states that every valid deduction (couched in the language of first-order predicate calculus with identity) is provable in the calculus. In other words, the deduction of B from premises \(A_{1}\), \(A_{2}\), … \(A_{n}\) (where statements \(A_{1}\), \(A_{2}\), … \(A_{n}\), B are all in the language of first-order predicate calculus with identity) is logically valid if and only if B can be proved from \(A_{1}\), \(A_{2}\), … \(A_{n}\) in the calculus.