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Computable analysis and effective descriptive set theory are both concernedwith complete metric spaces, functions between them and subsets thereof in aneffective setting. The precise relationship of the various definitions used inthe two disciplines has so far been neglected, a situation this paper is meantto remedy.  As the role of the Cauchy completion is relevant for both effectiveapproaches to Polish spaces, we consider the interplay of effectivity andcompletion in some more detail.

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