Theorems · Definition · logic and foundations

FirstOrder.Language.LHom.defaultExpansion

{L : FirstOrder.Language} →
  {L' : FirstOrder.Language} →
    (ϕ : L →ᴸ L') →
      [(n : ℕ) → (f : L'.Functions n) → Decidable (f ∈ Set.range fun f => ϕ.onFunction f)] →
        [(n : ℕ) → (r : L'.Relations n) → Decidable (r ∈ Set.range fun r => ϕ.onRelation r)] →
          (M : Type u_1) → [Inhabited M] → [L.Structure M] → L'.Structure M

Pulls an L-structure along a language map ϕ : L →ᴸ L', and then expands it to an L'-structure arbitrarily.

Defined in

Mathlib.ModelTheory.LanguageMap

Cited by

2 results in Mathlib

Foundations

Depth 17 from the axioms · uses Classical.choice

Assumes

DecidableDecidableInhabitedFirstOrder.Language.Structure