Ideas of Ernst Zermelo, by Theme

[German, 1871 - 1953, Professor at Göttingen, and then at Zurich.]

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2. Reason / D. Definition / 8. Impredicative Definition
 15924 Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them?
4. Formal Logic / F. Set Theory ST / 1. Set Theory
 17607 Set theory investigates number, order and function, showing logical foundations for mathematics
 17608 We take set theory as given, and retain everything valuable, while avoiding contradictions
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
 13012 Zermelo published his axioms in 1908, to secure a controversial proof
 17609 Set theory can be reduced to a few definitions and seven independent axioms
 9565 Zermelo made 'set' and 'member' undefined axioms
 3339 For Zermelo's set theory the empty set is zero and the successor of each number is its unit set
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
 13017 Zermelo introduced Pairing in 1930, and it seems fairly obvious
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
 13015 Zermelo used Foundation to block paradox, but then decided that only Separation was needed
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
 13020 The Axiom of Separation requires set generation up to one step back from contradiction
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
 17613 We should judge principles by the science, not science by some fixed principles
5. Theory of Logic / L. Paradox / 3. Antinomies
 17626 The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers
6. Mathematics / A. Nature of Mathematics / 3. Numbers / e. Ordinal numbers
 13487 In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / e. Countable infinity
 15897 Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed
6. Mathematics / B. Foundations for Mathematics / 5. Mathematics as Set Theory / a. Mathematics is set theory
 13027 Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets