more from William D. Hart

### Single Idea 13494

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets]

Full Idea

That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers).

Clarification

ZFC is the Zermelo-Fraenkel-with Choice system

Gist of Idea

The iterative conception may not be necessary, and may have fixed points or infinitely descending chains

Source

William D. Hart (The Evolution of Logic [2010], 3)

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.80

A Reaction

People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains.