10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) |

10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element |

10890 | A 'partial ordering' is reflexive, antisymmetric and transitive |

10886 | Determinacy: an object is either in a set, or it isn't |

10887 | Specification: Determinate totals of objects always make a set |

10897 | A first-order 'sentence' is a formula with no free variables |

10893 | Γ |= φ for sentences if φ is true when all of Γ is true |

10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations |

10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → |

10898 | The semantics shows how truth values depend on instantiations of properties and relations |

10902 | We can do semantics by looking at given propositions, or by building new ones |

10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another |

10895 | 'Logically true' (|= φ) is true for every truth-assignment |

10900 | Logically true sentences are true in all structures |

10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true |

10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true |

10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model |

10891 | If a set is defined by induction, then proof by induction can be applied to it |