Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.Sentence

FirstOrder.Language → Type (max u v)

A sentence is a formula with no free variables.

Defined in
Mathlib.ModelTheory.Syntax
Cited by
127 results in Mathlib
Foundations
Depth 5 from the axioms, rests on 9 definitions · uses no axioms
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FirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence.Realize · cited by 62Sentence.RealizeFirstOrder.Language.completeTheory · cited by 14Language.completeTheoryFirstOrder.Language.Formula.equivSentence · cited by 11Formula.equivSentenceFirstOrder.Language.Theory.IsComplete · cited by 11Theory.IsCompleteFirstOrder.Language.Theory.realize_sentence_of_mem · cited by 11Theory.realize_sentence_o…FirstOrder.Language.Theory.IsMaximal · cited by 10Theory.IsMaximalFirstOrder.Language.Theory.typesWith · cited by 9Theory.typesWithFirstOrder.Language.Theory.CompleteType.isMaximal · cited by 8CompleteType.isMaximalFirstOrder.Language.Theory.IsSatisfiable.mono · cited by 7IsSatisfiable.monoFirstOrder.Language.Theory.models_sentence_iff · cited by 6Theory.models_sentence_iffFirstOrder.Language.Sentence.realize_not · cited by 6Sentence.realize_notFirstOrder.Language.Theory.Model.mono · cited by 5Model.monoFirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentence · cited by 5ModelsBoundedFormula.real…FirstOrder.Language.denselyOrderedSentence · cited by 5Language.denselyOrderedSe…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Formula · cited by 93Language.FormulaLanguage.SentenceCITED BYCITES

Cites2

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Cited by160

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