 As a matter of fact the lemma has become the standard tool for producing self-referential statements and for transforming the semantical paradoxes into indefinability and (formal) undecidability results (see the entry on  self-reference).  The algebra underlying the Gödelian constructions will be grasped only much later during the 1970’s. It is also important to stress that a few years later (1938) an analog of the diagonalization lemma (the so-called second recursion theorem) was discovered by Kleene and was soon to become a basic tool in the foundations of recursion theory and computability theory.