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Theorems · Definition · logic and foundations

Cardinal.Categorical

{L : FirstOrder.Language} → Cardinal.{w} → L.Theory → Prop

A theory is κ-categorical if all models of size κ are isomorphic.

Defined in
Mathlib.ModelTheory.Satisfiability
Cited by
4 results in Mathlib
Foundations
Depth 20 from the axioms · uses Quot.sound
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Cardinal.Categorical.isComplete · cited by 3Categorical.isCompleteFirstOrder.Field.ACF_categorical · cited by 1Field.ACF_categoricalFirstOrder.Language.aleph0_categorical_dlo · cited by 1Language.aleph0_categoric…Cardinal.empty_theory_categorical · cited by 1Cardinal.empty_theory_cat…Cardinal · cited by 2598CardinalFirstOrder.Language · cited by 1084FirstOrder.LanguageCardinal.mk · cited by 942Cardinal.mkFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Equiv · cited by 83Language.EquivFirstOrder.Language.Theory.ModelType · cited by 62Theory.ModelTypeFirstOrder.Language.Theory.ModelType.Carrier · cited by 59ModelType.CarrierCardinal.CategoricalCITED BYCITES

Cites7

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Cited by4

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