Ideas from 'works' by Ernst Zermelo [1920], by Theme Structure
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9565

Zermelo made 'set' and 'member' undefined axioms




Full Idea:
The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given modeltheoretic analyses or definitions.




From:
report of Ernst Zermelo (works [1920]) by Charles Chihara  A Structural Account of Mathematics 7.5




A reaction:
This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics.

3339

For Zermelo's set theory the empty set is zero and the successor of each number is its unit set




Full Idea:
For Zermelo's set theory the empty set is zero and the successor of each number is its unit set.




From:
report of Ernst Zermelo (works [1920]) by Simon Blackburn  Oxford Dictionary of Philosophy p.280
