# Canonical effective subalgebras of classical algebras as constructive metric completions

## Jens Blanck

(Swansea)

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 realisability models. We work with general realisability 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.

**Thursday 10th December 2009, 14:00**

Far-134 (Video conferencing room)

Department of Computer Science