  computable functions are defined by abstract finite deterministic algorithms
on many-sorted algebras. We show that there exist finite universal algebraic
specifications that specify uniquely (up to isomorphism) (i) all abstract
computable functions on any many-sorted algebra; and (ii) all functions
effectively approximable by abstract computable functions on any metric
algebra.
  We show that there exist universal algebraic specifications for all the
classically computable functions on the set R of real numbers. The algebraic
specifications used are mainly bounded universal equations and conditional
equations. We investigate the initial algebra semantics of these
specifications, and derive situations where algebraic specifications define
precisely the computable functions.
