Bulletin of Symbolic Logic

Computable and continuous partial homomorphisms on metric partial algebras

Viggo Stoltenberg-Hansen and John V. Tucker

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations.

Article information

Bull. Symbolic Logic, Volume 09, Issue 3 (2003), 299- 334.

First available in Project Euclid: 17 July 2003

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Stoltenberg-Hansen, Viggo; Tucker, John V. Computable and continuous partial homomorphisms on metric partial algebras. Bull. Symbolic Logic 09 (2003), no. 3, 299-- 334. doi:10.2178/bsl/1058448675. https://projecteuclid.org/euclid.bsl/1058448675

Export citation