Definition for "Definable Closure" in the Quantum Dictionary

- Natural & Formal Sciences -

Mathematics & Logic Dictionary

Given a structure M and a subset A, the definable closure dcl(A) is the set of all elements of M that are uniquely specified (in M) by some first‑order formula with parameters from A; equivalently, elements fixed by every automorphism of M that fixes A pointwise.

- Pure Mathematics -

Algebra Dictionary

The definable closure dcl(A) of a set A in a structure M is the set of elements of M that are uniquely specified by some first-order formula with parameters from A; equivalently, b ∈ dcl(A) iff there is a formula φ(x,a) with a from A such that M ⊨ φ(b,a) and M ⊨ ∀x(φ(x,a) → x=b).