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Theorems · Theorem · logic and foundations

FirstOrder.Language.completeTheory.mem_or_not_mem

∀ (L : FirstOrder.Language) (M : Type w) [inst : L.Structure M] (φ : L.Sentence),
  φ ∈ L.completeTheory M ∨ FirstOrder.Language.Formula.not φ ∈ L.completeTheory M
Defined in
Mathlib.ModelTheory.Satisfiability
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.Structure
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FirstOrder.Language.completeTheory.isMaximal · cited by 2completeTheory.isMaximalFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.Formula · cited by 93Language.FormulaFirstOrder.Language.Formula.Realize · cited by 81Formula.RealizeFirstOrder.Language.Formula.not · cited by 27Formula.notFirstOrder.Language.completeTheory · cited by 14Language.completeTheorycompleteTheory.mem_or_not_memCITED BYCITES

Cites8

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Cited by1

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