The unwind property in certain algebras

Abstract

In the present paper we investigate abstract algebras having the so-called unwind property, i.e., algebras where every total computable function can be defined by open formulas in an adequate first-order language. A method of proving the unwind property is given for a special kind of algebra. Applying this method we prove that there exists a structure satisfying the unwind property for all flow charts, but not for recursive procedures. We prove also that algebraically closed and real closed fields with infinite degrees of transcendence over their prime subfields satisfy the unwind property for all schemas.