Full Idea
It was observed by several people that for a satisfactory theory of ordinal numbers, Zermelo's axioms required strengthening. The Axiom of Replacement was proposed by Fraenkel and others, giving rise to the Zermelo-Fraenkel (ZF) axioms.
Gist of Idea
Fraenkel added Replacement, to give a theory of ordinal numbers
Source
Herbert B. Enderton (Elements of Set Theory [1977], 1:15)
Book Reference
Enderton,Herbert B.: 'Elements of Set Theory' [Posts + Telecoms 2006], p.18
Related Ideas
Idea 15933 Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine]
Idea 15945 Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine]