Theorems · Theorem · logic and foundations
FirstOrder.Language.card_le_of_model_distinctConstantsTheory
∀ (L : FirstOrder.Language) {α : Type u'} (s : Set α) (M : Type w) [inst : (L.withConstants α).Structure M]
[h : M ⊨ L.distinctConstantsTheory s], Cardinal.lift.{w, u'} (Cardinal.mk ↑s) ≤ Cardinal.lift.{u', w} (Cardinal.mk M)- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- FirstOrder.Languagestatement and proof · cited by 1,084
- Cardinal.mkstatement · cited by 942
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Cardinal.liftstatement · cited by 583
- Set.domRestrictproof · cited by 383
- FirstOrder.Language.withConstantsstatement and proof · cited by 108
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.constantMapproof · cited by 28
- FirstOrder.Language.conproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.exists_large_model_of_infinite_modelproof · cited by 1