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Theorems · Theorem · logic and foundations

FirstOrder.Language.Theory.models_sentence_of_mem

∀ {L : FirstOrder.Language} {T : L.Theory} {φ : L.Sentence}, φ ∈ T → T ⊨ᵇ φ
Defined in
Mathlib.ModelTheory.Satisfiability
Cited by
3 results in Mathlib
Foundations
Depth 25 from the axioms · uses Quot.sound
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FirstOrder.Language.Theory.IsMaximal.mem_iff_models · cited by 3IsMaximal.mem_iff_modelsFirstOrder.Language.Theory.IsMaximal.isComplete · cited by 2IsMaximal.isCompleteFirstOrder.Field.finite_ACF_prime_not_realize_of_ACF_zero_realize · cited by 2Field.finite_ACF_prime_no…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.Theory.ModelType · cited by 62Theory.ModelTypeFirstOrder.Language.Theory.ModelsBoundedFormula · cited by 30Theory.ModelsBoundedFormu…FirstOrder.Language.Theory.realize_sentence_of_mem · cited by 11Theory.realize_sentence_o…FirstOrder.Language.Theory.models_sentence_iff · cited by 6Theory.models_sentence_iffTheory.models_sentence_of_memCITED BYCITES

Cites7

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Cited by3

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