Stability for Effective Algebras

We give a general method for showing that all numberings of certain effective algebras are recursively equivalent. The method is based on computable approximation-limit pairs. The approximations are elements of a finitely generated subalgebra, and obtained by computable (non-deterministic) selection. The results are a continuation of the work by Mal'cev, who, for example, showed that finitely generated semicomputable algebras are computably stable. In particular, we generalise the result that the recursive reals are computably stable, if the limit operator is assumed to be computable, to spaces constructed by inverse limits.