Single Idea 17609

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets]

Full Idea

I intend to show how the entire theory created by Cantor and Dedekind can be reduced to a few definitions and seven principles, or axioms, which appear to be mutually independent.

Gist of Idea

Set theory can be reduced to a few definitions and seven independent axioms

Source

Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro)

Book Reference

'From Frege to Gödel 1879-1931', ed/tr. Heijenoort,Jean van [Harvard 1967], p.200


A Reaction

The number of axioms crept up to nine or ten in subsequent years. The point of axioms is maximum reduction and independence from one another. He says nothing about self-evidence (though Boolos claimed a degree of that).