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
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9565
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Zermelo made 'set' and 'member' undefined axioms
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Full Idea:
The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given model-theoretic analyses or definitions.
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From:
report of Ernst Zermelo (works [1920]) by Charles Chihara - A Structural Account of Mathematics 7.5
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A reaction:
This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics.
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3339
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For Zermelo's set theory the empty set is zero and the successor of each number is its unit set
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Full Idea:
For Zermelo's set theory the empty set is zero and the successor of each number is its unit set.
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From:
report of Ernst Zermelo (works [1920]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280
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