10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned |

10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) |

10478 | Since first-order languages are complete, |= and |- have the same meaning |

10477 | |= in model-theory means 'logical consequence' - it holds in all models |

10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables |

10284 | There are three different standard presentations of semantics |

10285 | I |= φ means that the formula φ is true in the interpretation I |

10474 | |= should be read as 'is a model for' or 'satisfies' |

10473 | Model theory studies formal or natural language-interpretation using set-theory |

10475 | A 'structure' is an interpretation specifying objects and classes of quantification |

10481 | Models in model theory are structures, not sets of descriptions |

10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models |

10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model |

10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it |

10480 | First-order logic can't discriminate between one infinite cardinal and another |

10286 | A 'set' is a mathematically well-behaved class |