15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? |

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 |

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 |

13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious |

13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed |

13020 | The Axiom of Separation requires set generation up to one step back from contradiction |

17613 | We should judge principles by the science, not science by some fixed principles |

17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers |

13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals |

15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed |

13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets |