Theorems · Definition · logic and foundations

FirstOrder.Language.ElementaryEmbedding.ofModelsElementaryDiagram

(L : FirstOrder.Language) →
  (M : Type u_1) →
    [inst : L.Structure M] →
      (N : Type u_5) →
        [inst_1 : L.Structure N] →
          [inst_2 : (L.withConstants M).Structure N] →
            [(L.lhomWithConstants M).IsExpansionOn N] → [N ⊨ L.elementaryDiagram M] → L.ElementaryEmbedding M N

The canonical elementary embedding of an L-structure into any model of its elementary diagram

Defined in

Mathlib.ModelTheory.ElementaryMaps

Cited by

2 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.StructureFirstOrder.Language.StructureFirstOrder.Language.LHom.IsExpansionOnFirstOrder.Language.Theory.Model