Jens Blanck and I presented a paper at Computability and Complexity in Analysis 2009 with a complicated title (I like complicated titles):

Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions

which has been published in Volume 16, Issue 18 of the Journal of Universal Computer Science. I usually just post the abstract, but this time I would like to explain the general idea informally, the way one can do it on a blog. But first, here is the abstract:

**Abstract:** We prove general theorems about unique existence of effective subalgebras of classical algebras. The theorems are consequences of standard facts about completions of metric spaces within the framework of constructive mathematics, suitably interpreted in realizability models. We work with general realizability models rather than with a particular model of computation. Consequently, all the results are applicable in various established schools of computability, such as type 1 and type 2 effectivity, domain representations, equilogical spaces, and others.

**Download paper:** effalg.pdf or directly from JUCS