Admissible representations in computable analysis

Authors:
Matthias Schröder
Affiliations:
LFCS, School of Informatics, University of Edinburgh, Edinburgh, UK
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

Citing 12
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Abstract

Computable Analysis investigates computability on real numbers and related spaces. One approach to Computable Analysis is Type Two Theory of Effectivity (TTE). TTE provides a computational framework for non-discrete spaces with cardinality of the continuum. Its basic tool are representations. A representation equips the objects of a given space with “names”, which are infinite words. Computations are performed on these names. We discuss the property of admissibility as a well-behavedness criterion for representations. Moreover we investigate and characterise the class of spaces which have such an admissible representation. This category turns out to have a remarkably rich structure.