age — Mathlib

English

The age of a structure M is the class of all finitely generated L-structures N that embed into M.

Русский

Возраст структуры M является классом всех finitely generated L-структур N, которые вложиваются в M.

LaTeX

$$$\mathrm{age}_L(M) = \{ N : \text{Bundled } L\text{-Structure} \mid \mathrm{FG}_L(N) \wedge \exist \iota: N \hookrightarrow_L M\}$$$

Lean4

/-- The age of a structure `M` is the class of finitely-generated structures that embed into it. -/
def age (M : Type w) [L.Structure M] : Set (Bundled.{w} L.Structure) :=
  {N | Structure.FG L N ∧ Nonempty (N ↪[L] M)}

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