Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.partialOrderOfModels

(L : FirstOrder.Language) →
  (M : Type w') → [inst : L.IsOrdered] → [inst_1 : L.Structure M] → [h : M ⊨ L.partialOrderTheory] → PartialOrder M

Any model of a theory of partial orders is a partial order.

Defined in
Mathlib.ModelTheory.Order
Cited by
0 results in Mathlib
Foundations
Depth 38 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.IsOrderedFirstOrder.Language.StructureFirstOrder.Language.Theory.Model
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FirstOrder.Language.linearOrderOfModels · cited by 2Language.linearOrderOfMod…Preorder · cited by 7952PreorderPartialOrder · cited by 6410PartialOrderFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.IsOrdered · cited by 19Language.IsOrderedFirstOrder.Language.partialOrderTheory · cited by 0Language.partialOrderTheo…FirstOrder.Language.preorderOfModels · cited by 0Language.preorderOfModelsLanguage.partialOrderOfModelsCITED BYCITES

Cites8

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Cited by1

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