Theorems · Theorem · logic and foundations
FirstOrder.Language.model_infiniteTheory_iff
∀ (L : FirstOrder.Language) {M : Type w} [inst : L.Structure M], M ⊨ L.infiniteTheory ↔ Infinite M- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangeproof · cited by 4,705
- FirstOrder.Languagestatement and proof · cited by 1,084
- Cardinal.mkproof · cited by 942
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Infinitestatement · cited by 352
- FirstOrder.Language.Sentenceproof · cited by 127
- FirstOrder.Language.Theory.Modelstatement · cited by 67
- FirstOrder.Language.Sentence.Realizeproof · cited by 62
- FirstOrder.Language.Sentence.cardGeproof · cited by 3
- FirstOrder.Language.infiniteTheorystatement · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.ElementarilyEquivalent.infinite_iffproof · cited by 1
- Cardinal.empty_infinite_Theory_isCompleteproof · cited by 0