Algebraic Closure (Model-Theoretic)

- Pure Mathematics -
Algebra Dictionary
Definition
In a given first-order structure or model M and for a parameter set A ⊆ M, the model-theoretic algebraic closure acl(A) is the set of all elements of M that satisfy some formula with parameters from A that has only finitely many solutions in M. It is a closure operator capturing finite definability over A in the model-theoretic sense.