Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.isSatisfiable_union_distinctConstantsTheory_of_infinite
∀ {L : FirstOrder.Language} {α : Type w} (T : L.Theory) (s : Set α) (M : Type w') [inst : L.Structure M] [M ⊨ T]
[Infinite M], ((L.lhomWithConstants α).onTheory T ∪ L.distinctConstantsTheory s).IsSatisfiable- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- Monotoneproof · cited by 1,397
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Finset.mapproof · cited by 747
- Infinitestatement and proof · cited by 352
- FirstOrder.Language.Theorystatement and proof · cited by 154
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.exists_large_model_of_infinite_modelproof · cited by 1