## First order categorical logic: model-theoretical methods in the theory of topoi and related categories |

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### Contents

Grothendieck topoi ll | 11 |

Interpretation of the logic L | 68 |

Axioms and rules of inference valid | 96 |

Copyright | |

7 other sections not shown

### Common terms and phrases

A-finite A-logical A-recursive arbitrary assume atomic formula axioms c.f. Chapter canonical injections canonical topology category of sheaves classifying topos coherent objects coherent topos commutative diagram compatible family complete Boolean algebra completeness theorem composition consider construction countable Cov(A covering family defined definition denote disjoint sum domain E-model effective epimorphic family elements equivalence relation exists fact finitary finitary coherent finite left limits follows fragment F free variables full subcategory functor category given Grothendieck topology Grothendieck topos H-valued hence Heyting homomorphism hypothesis induction infinitary infs isomorphism K-logical left limit diagram LEMMA logical category logical functor monomorphism natural transformation notation notion ob(C ob(R obtain operation symbol premorphism preserves finite left presheaf pretopos proof PROPOSITION pullback pullback diagram quotient regular cardinal REMARK S(aQ satisfies Section sequents SGA4 sheaf stable effective stably distributive subobject subset surjective topoi unique universal property Vf(X