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Theorems · Theorem · logic and foundations

FirstOrder.Language.ElementarilyEquivalent.nonempty

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N]
  [Mn : Nonempty M], L.ElementarilyEquivalent M N → Nonempty N
Defined in
Mathlib.ModelTheory.Semantics
Cited by
1 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.StructureNonempty
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FirstOrder.Language.Theory.exists_model_card_eq · cited by 1Theory.exists_model_card_…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.ElementarilyEquivalent · cited by 19Language.ElementarilyEqui…FirstOrder.Language.ElementarilyEquivalent.nonempty_iff · cited by 1ElementarilyEquivalent.no…ElementarilyEquivalent.nonemp…CITED BYCITES

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