Algebraic type

A complete type is algebraic when it contains a formula having finitely many realizations in a model of the theory. A one-element example is the type containing $x=c$ for a named constant. Such a type cannot gain infinitely many realizations in an elementarily equivalent structure. An isolated type need not be algebraic: the unique empty-set one-type in a dense linear order without endpoints is isolated by $x=x$ and has infinitely many realizations.