Theorems · Theorem · logic and foundations
FirstOrder.Language.StrongHomClass.realize_sentence
∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] {F : Type u_4}
[inst_2 : EquivLike F M N] [L.StrongHomClass F M N] (g : F) (φ : L.Sentence), M ⊨ φ ↔ N ⊨ φ- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, 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.
- DFunLike.coeproof · cited by 62,936
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- EquivLikestatement and proof · cited by 165
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- FirstOrder.Language.Formula.Realizeproof · cited by 81
- FirstOrder.Language.Sentence.Realizestatement and proof · cited by 62
- Unique.eq_defaultproof · cited by 38
- FirstOrder.Language.StrongHomClassstatement and proof · cited by 16
- FirstOrder.Language.StrongHomClass.realize_formulaproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.Categorical.isCompleteproof · cited by 3
- FirstOrder.Language.StrongHomClass.elementarilyEquivalentproof · cited by 0
- FirstOrder.Language.StrongHomClass.theory_modelproof · cited by 0