Mathlib Map

Theorems · Inductive type · logic and foundations

FirstOrder.Language.Theory.IsUniversal

{L : FirstOrder.Language} → L.Theory → Prop

A theory is universal when it is comprised only of universal sentences - these theories apply also to substructures.

Defined in
Mathlib.ModelTheory.Complexity
Cited by
3 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
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Around this declaration

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

FirstOrder.Language.Theory.IsUniversal.isUniversal_of_mem · cited by 2IsUniversal.isUniversal_o…FirstOrder.Language.Theory.IsUniversal.models_of_embedding · cited by 1IsUniversal.models_of_emb…FirstOrder.Language.Theory.IsUniversal.casesOn · cited by 0IsUniversal.casesOnFirstOrder.Language.Theory.IsUniversal.insert · cited by 0IsUniversal.insertFirstOrder.Language.Theory.IsUniversal.recOn · cited by 0IsUniversal.recOnFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Theory · cited by 154Language.TheoryTheory.IsUniversalCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.