Theorems · Theorem · logic and foundations
FirstOrder.Language.ElementarilyEquivalent.infinite
∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N]
[Mi : Infinite M], L.ElementarilyEquivalent M N → Infinite N- Defined in
- Mathlib.ModelTheory.Semantics
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- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Infinitestatement and proof · cited by 352
- FirstOrder.Language.ElementarilyEquivalentstatement and proof · cited by 19
- FirstOrder.Language.ElementarilyEquivalent.infinite_iffproof · cited by 1
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