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Theorems · Theorem · logic and foundations

FirstOrder.Language.ElementarilyEquivalent.theory_model_iff

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] {T : L.Theory},
  L.ElementarilyEquivalent M N → (M ⊨ T ↔ N ⊨ T)
Defined in
Mathlib.ModelTheory.Semantics
Cited by
3 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure
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FirstOrder.Language.ElementarilyEquivalent.theory_model · cited by 1ElementarilyEquivalent.th…FirstOrder.Language.ElementarilyEquivalent.infinite_iff · cited by 1ElementarilyEquivalent.in…FirstOrder.Language.ElementarilyEquivalent.nonempty_iff · cited by 1ElementarilyEquivalent.no…FirstOrder.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.ElementarilyEquivalent · cited by 19Language.ElementarilyEqui…FirstOrder.Language.completeTheory · cited by 14Language.completeTheoryFirstOrder.Language.Theory.model_iff_subset_completeTheory · cited by 2Theory.model_iff_subset_c…FirstOrder.Language.ElementarilyEquivalent.completeTheory_eq · cited by 1ElementarilyEquivalent.co…ElementarilyEquivalent.theory…CITED BYCITES

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