Model theoretic algebraic closure
If M is a first-order structure,
A ⊆ M is a subset
of its universe, and a ∈ M is an element of M, then we say
that a is algebraic over A, or a ∈ acl(A), if
there is a formula φ(x) with parameters from A so that φ(a) holds
but
φ(M) = { b ∈ M | φ(b) }
is finite.
In the case that M is an algebraically
closed field, acl(A) is the algebraic closure (in the usual field
theoretic sense) of the field generated by A.