Full Idea
Zermelo-Fraenkel axioms: Existence (at least one set); Extension (same elements, same set); Specification (a condition creates a new set); Pairing (two sets make a set); Unions; Powers (all subsets make a set); Infinity (set of successors); Choice
Gist of Idea
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice
Source
report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15
Book Reference
Clegg,Brian: 'Infinity' [Robinson 2003], p.205