Ideas from 'Investigations in the Foundations of Set Theory I' by Ernst Zermelo [1908], by Theme Structure

[found in 'From Frege to Gödel 1879-1931' (ed/tr Heijenoort,Jean van) [Harvard 1967,0-674-32449-8]].

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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? [Lavine]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
 17608 We take set theory as given, and retain everything valuable, while avoiding contradictions
 17607 Set theory investigates number, order and function, showing logical foundations for mathematics
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
 10870 ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Clegg]
 13012 Zermelo published his axioms in 1908, to secure a controversial proof [Maddy]
 17609 Set theory can be reduced to a few definitions and seven independent axioms
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 [Maddy]
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 [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
 13486 Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Hart,WD]
 13020 The Axiom of Separation requires set generation up to one step back from contradiction [Maddy]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
 13487 In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
 18178 For Zermelo the successor of n is {n} (rather than n U {n}) [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
 13027 Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
 9627 Different versions of set theory result in different underlying structures for numbers [Brown,JR]