Mathlib Map

Theorems · Inductive type · logic and foundations

FirstOrder.Language.OrderedStructure

(L : FirstOrder.Language) → (M : Type w') → [L.IsOrdered] → [LE M] → [L.Structure M] → Prop

A structure is ordered if its language has a ≤ symbol whose interpretation is ≤.

Defined in
Mathlib.ModelTheory.Order
Cited by
16 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
FirstOrder.Language.IsOrderedLEFirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.realize_denselyOrdered_iff · cited by 2Language.realize_denselyO…FirstOrder.Language.realize_noBotOrder_iff · cited by 2Language.realize_noBotOrd…FirstOrder.Language.realize_noTopOrder_iff · cited by 2Language.realize_noTopOrd…FirstOrder.Language.HomClass.monotone · cited by 1HomClass.monotoneFirstOrder.Language.HomClass.strictMono · cited by 1HomClass.strictMonoFirstOrder.Language.denselyOrdered_of_dlo · cited by 1Language.denselyOrdered_o…FirstOrder.Language.noBotOrder_of_dlo · cited by 1Language.noBotOrder_of_dloFirstOrder.Language.noTopOrder_of_dlo · cited by 1Language.noTopOrder_of_dloFirstOrder.Language.orderedStructure_iff · cited by 0Language.orderedStructure…FirstOrder.Language.realize_denselyOrdered · cited by 0Language.realize_denselyO…FirstOrder.Language.Term.realize_le · cited by 0Term.realize_leFirstOrder.Language.realize_noBotOrder · cited by 0Language.realize_noBotOrd…FirstOrder.Language.realize_noTopOrder · cited by 0Language.realize_noTopOrd…FirstOrder.Language.Term.realize_lt · cited by 0Term.realize_ltFirstOrder.Language.StrongHomClass.toOrderIsoClass · cited by 0StrongHomClass.toOrderIso…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.IsOrdered · cited by 19Language.IsOrderedLanguage.OrderedStructureCITED BYCITES

Cites3

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Cited by18

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