Computability in Europe 2006
Logical Approaches to Computational Barriers

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Special Session Talk:
Admissible Representations in Computable Analysis

Speaker: Matthias Schroeder
Presentation: schroedertalk.ps

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. 


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