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### Ideas of Ernst Zermelo, by Text

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

 1904 Proof that every set can be well-ordered
 p.4 15897 Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed
 1908 Investigations in the Foundations of Set Theory I
 p.70 13487 In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals
 p.107 15924 Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them?
 p.483 13012 Zermelo published his axioms in 1908, to secure a controversial proof
 p.484 13017 Zermelo introduced Pairing in 1930, and it seems fairly obvious
 p.484 13015 Zermelo used Foundation to block paradox, but then decided that only Separation was needed
 p.485 13020 The Axiom of Separation requires set generation up to one step back from contradiction
 p.489 13027 Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets
 Intro p.200 17609 Set theory can be reduced to a few definitions and seven independent axioms
 Intro p.200 17608 We take set theory as given, and retain everything valuable, while avoiding contradictions
 Intro p.200 17607 Set theory investigates number, order and function, showing logical foundations for mathematics
 1908 New Proof of Possibility of Well-Ordering
 §2a p.189 17613 We should judge principles by the science, not science by some fixed principles
 1920 works
 p.204 9565 Zermelo made 'set' and 'member' undefined axioms
 p.280 3339 For Zermelo's set theory the empty set is zero and the successor of each number is its unit set
 1930 On boundary numbers and domains of sets
 §5 p.1233 17626 The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers