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Theorems · Theorem · logic and foundations

FirstOrder.Language.Theory.CompleteType.false_of_mem_of_not_mem

∀ {L : FirstOrder.Language} {T : L.Theory},
  T.IsSatisfiable → ∀ {φ : L.Sentence}, φ ∈ T → FirstOrder.Language.BoundedFormula.not φ ∈ T → False
Defined in
Mathlib.ModelTheory.Types
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0 results in Mathlib
Foundations
Depth 24 from the axioms · uses Quot.sound
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FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.Theory.ModelType · cited by 62Theory.ModelTypeFirstOrder.Language.BoundedFormula.not · cited by 27BoundedFormula.notFirstOrder.Language.Theory.IsSatisfiable · cited by 25Theory.IsSatisfiableFirstOrder.Language.Theory.Model.realize_of_mem · cited by 3Model.realize_of_memCompleteType.false_of_mem_of_…CITED BYCITES

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