Full Idea
Zermelo realised that the Axiom of Choice (based on arbitrary functions) could be used to 'count', in the Cantorian sense, those collections that had given Cantor so much trouble, which restored a certain unity to set theory.
Gist of Idea
Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed
Source
report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I
Book Reference
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.4
Related Idea
Idea 15896 Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]