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A comparison of concepts from computable analysis and effective descriptive set theory (1403.7997v2)
Published 31 Mar 2014 in cs.LO and math.GN
Abstract: 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.