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Theorems · Theorem · logic and foundations

FirstOrder.Language.Theory.IsUniversal.models_of_embedding

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {T : L.Theory} [hT : T.IsUniversal] {N : Type u_1}
  [inst_1 : L.Structure N] [N ⊨ T] (f : L.Embedding M N), M ⊨ T
Defined in
Mathlib.ModelTheory.Complexity
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Theory.IsUniversalFirstOrder.Language.StructureFirstOrder.Language.Theory.Model
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FirstOrder.Language.dlo_age · cited by 1Language.dlo_ageDFunLike.coe · cited by 62936DFunLike.coeFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Embedding · cited by 128Language.EmbeddingFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.BoundedFormula.Realize · cited by 104BoundedFormula.RealizeFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.Theory.realize_sentence_of_mem · cited by 11Theory.realize_sentence_o…FirstOrder.Language.Theory.IsUniversal · cited by 3Theory.IsUniversalFirstOrder.Language.Theory.IsUniversal.isUniversal_of_mem · cited by 2IsUniversal.isUniversal_o…FirstOrder.Language.BoundedFormula.IsUniversal.realize_embedding · cited by 1IsUniversal.realize_embed…IsUniversal.models_of_embeddi…CITED BYCITES

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