Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.CompleteType.setOfPred_mem_eq_univ_iff
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} (φ : (L.withConstants α).Sentence),
{p | φ ∈ p} = Set.univ ↔ (L.lhomWithConstants α).onTheory T ⊨ᵇ φ- Defined in
- Mathlib.ModelTheory.Types
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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.ofPredstatement and proof · cited by 6,101
- Set.univstatement and proof · cited by 3,945
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- FirstOrder.Language.withConstantsstatement and proof · cited by 108
- FirstOrder.Language.lhomWithConstantsstatement and proof · cited by 39
- FirstOrder.Language.Theory.CompleteTypestatement and proof · cited by 35
- FirstOrder.Language.Theory.ModelsBoundedFormulastatement · cited by 30
- FirstOrder.Language.LHom.onTheorystatement and proof · cited by 27
- FirstOrder.Language.Formula.notproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.CompleteType.setOf_mem_eq_univ_iffproof · cited by 0