 Theorem 2 (Gödel’s Fixed Point Theorem)  If φ(v0) is a formula of number theory, then there is a sentence ψ such that P ⊢ ψ ↔ φ(⌈ψ⌉), where ⌈ψ⌉ is the formal term corresponding to the natural number code of ⌈ψ⌉.