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Theorems · Theorem · logic and foundations

FirstOrder.Language.ElementarilyEquivalent.infinite_iff

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N],
  L.ElementarilyEquivalent M N → (Infinite M ↔ Infinite N)
Defined in
Mathlib.ModelTheory.Semantics
Cited by
1 results in Mathlib
Foundations
Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure
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FirstOrder.Language.ElementarilyEquivalent.infinite · cited by 0ElementarilyEquivalent.in…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureInfinite · cited by 352InfiniteFirstOrder.Language.ElementarilyEquivalent · cited by 19Language.ElementarilyEqui…FirstOrder.Language.ElementarilyEquivalent.theory_model_iff · cited by 3ElementarilyEquivalent.th…FirstOrder.Language.model_infiniteTheory_iff · cited by 2Language.model_infiniteTh…ElementarilyEquivalent.infini…CITED BYCITES

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