Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.IsMaximal.mem_iff_models
∀ {L : FirstOrder.Language} {T : L.Theory}, T.IsMaximal → ∀ (φ : L.Sentence), φ ∈ T ↔ T ⊨ᵇ φ- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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.Theory.ModelsBoundedFormulastatement · cited by 30
- FirstOrder.Language.Theory.IsMaximalstatement and proof · cited by 10
- FirstOrder.Language.Theory.models_sentence_of_memproof · cited by 3
- FirstOrder.Language.Theory.IsMaximal.mem_of_modelsproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.CompleteType.typesWith_infproof · cited by 1
- FirstOrder.Language.Theory.CompleteType.toList_foldr_inf_memproof · cited by 0
- FirstOrder.Language.Theory.exists_modelType_is_realized_inproof · cited by 0