User:IssaRice/Computability and logic/Diagonalization lemma

Rogers's fixed point theorem

Let $f$ be a total computable function. Then there exists an index $e$ such that ${\phi }_e\simeq {\phi }_{f(e)}$.

Diagonalization lemma

Let $A$ be a formula with one free variable. Then there exists a sentence $G$ such that $G$ iff $A(⌜G⌝)$.