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A comparison of concepts from computable analysis and effective descriptive set theory

Published online by Cambridge University Press:  23 June 2016

VASSILIOS GREGORIADES ,
TAMÁS KISPÉTER  and
ARNO PAULY
VASSILIOS GREGORIADES
Affiliation:
Department of Mathematics, Technische Universität Darmstadt, Darmstadt, Germany Email: gregoriades@mathematik.tu-darmstadt.de
TAMÁS KISPÉTER
Affiliation:
Computer Laboratory, University of Cambridge, Cambridge, U.K. Email: tk407@cam.ac.uk, Arno.Pauly@cl.cam.ac.uk
ARNO PAULY
Affiliation:
Computer Laboratory, University of Cambridge, Cambridge, U.K. Email: tk407@cam.ac.uk, Arno.Pauly@cl.cam.ac.uk
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Abstract

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Computable analysis and effective descriptive set theory are both concerned with complete metric spaces, functions between them and subsets thereof in an effective setting. The precise relationship of the various definitions used in the two disciplines has so far been neglected, a situation this paper is meant to remedy.

As the role of the Cauchy completion is relevant for both effective approaches to Polish spaces, we consider the interplay of effectivity and completion in some more detail.

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