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Theorems · Theorem · logic and foundations

FirstOrder.Language.Theory.Model.isSatisfiable

∀ {L : FirstOrder.Language} {T : L.Theory} (M : Type w) [Nonempty M] [inst : L.Structure M] [M ⊨ T], T.IsSatisfiable
Defined in
Mathlib.ModelTheory.Satisfiability
Cited by
5 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonemptyFirstOrder.Language.StructureFirstOrder.Language.Theory.Model
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FirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentence · cited by 5ModelsBoundedFormula.real…FirstOrder.Language.Theory.isSatisfiable_of_isSatisfiable_onTheory · cited by 1Theory.isSatisfiable_of_i…FirstOrder.Language.Theory.isSatisfiable_onTheory_iff · cited by 1Theory.isSatisfiable_onTh…FirstOrder.Language.Theory.isSatisfiable_union_distinctConstantsTheory_of_card_le · cited by 1Theory.isSatisfiable_unio…FirstOrder.Language.completeTheory.isSatisfiable · cited by 1completeTheory.isSatisfia…Bot.bot · cited by 4720Bot.botFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.Theory.IsSatisfiable · cited by 25Theory.IsSatisfiableFirstOrder.Language.Substructure.elementarySkolem₁Reduct · cited by 4Substructure.elementarySk…FirstOrder.Language.Theory.ModelType.shrink · cited by 1ModelType.shrinkFirstOrder.Language.ElementarySubstructure.toModel · cited by 1ElementarySubstructure.to…Model.isSatisfiableCITED BYCITES

Cites9

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Cited by5

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