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Theorems · Theorem · logic and foundations

FirstOrder.Language.ElementarySubstructure.realize_sentence

∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] (S : L.ElementarySubstructure M) (φ : L.Sentence),
  ↥S ⊨ φ ↔ M ⊨ φ
Defined in
Mathlib.ModelTheory.ElementarySubstructures
Cited by
0 results in Mathlib
Foundations
Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.Structure
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FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.Sentence.Realize · cited by 62Sentence.RealizeFirstOrder.Language.ElementarySubstructure · cited by 18Language.ElementarySubstr…FirstOrder.Language.ElementarySubstructure.subtype · cited by 7ElementarySubstructure.su…FirstOrder.Language.ElementaryEmbedding.map_sentence · cited by 3ElementaryEmbedding.map_s…ElementarySubstructure.realiz…CITED BYCITES

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