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Theorems · Theorem · logic and foundations

FirstOrder.Language.noTopOrder_of_dlo

∀ (L : FirstOrder.Language) (M : Type w') [inst : L.IsOrdered] [inst_1 : L.Structure M] [inst_2 : LE M]
  [L.OrderedStructure M] [M ⊨ L.dlo], NoTopOrder M
Defined in
Mathlib.ModelTheory.Order
Cited by
1 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.IsOrderedFirstOrder.Language.StructureLEFirstOrder.Language.OrderedStructureFirstOrder.Language.Theory.Model
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FirstOrder.Language.dlo_isExtensionPair · cited by 1Language.dlo_isExtensionP…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureSet.union_singleton · cited by 107Set.union_singletonFirstOrder.Language.Theory.Model · cited by 67Theory.ModelNoTopOrder · cited by 50NoTopOrderFirstOrder.Language.IsOrdered · cited by 19Language.IsOrderedFirstOrder.Language.OrderedStructure · cited by 16Language.OrderedStructureSet.union_insert · cited by 11Set.union_insertFirstOrder.Language.Theory.realize_sentence_of_mem · cited by 11Theory.realize_sentence_o…FirstOrder.Language.dlo · cited by 8Language.dloFirstOrder.Language.linearOrderTheory · cited by 7Language.linearOrderTheoryFirstOrder.Language.denselyOrderedSentence · cited by 5Language.denselyOrderedSe…FirstOrder.Language.noBotOrderSentence · cited by 5Language.noBotOrderSenten…FirstOrder.Language.noTopOrderSentence · cited by 5Language.noTopOrderSenten…FirstOrder.Language.realize_noTopOrder_iff · cited by 2Language.realize_noTopOrd…Language.noTopOrder_of_dloCITED BYCITES

Cites15

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