more from Herbert B. Enderton

### Single Idea 13202

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII]

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]**