10147 | The Axiom of Choice is consistent with the other axioms of set theory |

10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy |

10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets |

10150 | The Trichotomy Principle is equivalent to the Axiom of Choice |

10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition |

10162 | Tarski and Vaught established the equivalence relations between first-order structures |

10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? |

10160 | Löwenheim-Skolem says if the sentences are countable, so is the model |

10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory |

10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory |

10156 | 'Recursion theory' concerns what can be solved by computing machines |

10155 | Both Principia Mathematica and Peano Arithmetic are undecidable |

10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics |