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15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Lavine] |
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 |
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 |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Maddy] |
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] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Hart,WD] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Brown,JR] |