17749 | Post proved the consistency of propositional logic in 1921 |

17765 | Propositional language can only relate statements as the same or as different |

17764 | Boolean connectives are interpreted as functions on the set {1,0} |

17751 | Gödel proved the completeness of first order predicate logic in 1930 |

17752 | The empty set is useful for defining sets by properties, when the members are not yet known |

17753 | The empty set avoids having to take special precautions in case members vanish |

17759 | Ordinals play the central role in set theory, providing the model of well-ordering |

17741 | To determine the patterns in logic, one must identify its 'building blocks' |

17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true |

17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory |

17761 | A compact axiomatisation makes it possible to understand a field as a whole |

17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation |

17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... |

17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals |

17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion |

17760 | Two infinite ordinals can represent a single infinite cardinal |

17757 | Members of ordinals are ordinals, and also subsets of ordinals |

17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate |

17754 | Inductive proof depends on the choice of the ordering |

17742 | Scotus based modality on semantic consistency, instead of on what the future could allow |