### Single Idea 15524

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers]

Full Idea

What sets Zermelo's modelling of arithmetic apart from von Neumann's and all the rest is that he identifies the primitive of arithmetic with an appropriately primitive notion of set theory.

Gist of Idea

Zermelo's model of arithmetic is distinctive because it rests on a primitive of set theory

Source

David Lewis (Parts of Classes [1991], 4.6)

Book Reference

Lewis,David: 'Parts of Classes' [Blackwell 1991], p.111

A Reaction

Zermelo's model is just endlessly nested empty sets, which is a very simple structure. I gather that connoisseurs seem to prefer von Neumann's model (where each number contains its predecessor number).