A comparison of concepts from computable analysis and effective descriptive set theory. (23rd June 2016)

• Record Type: Journal Article
• Authors: GREGORIADES, VASSILIOS; KISPÉTER, TAMÁS; PAULY, ARNO
• Is Part Of: Mathematical structures in computer science. Volume 27:Number 8(2017)
• Page Start: 1414
• Page End: 1436
• Publication Date: 2016-06-23
• Subjects: Computer science -- Mathematics -- Periodicals; 004.015105
• DOI: 10.1017/S0960129516000128
• Languages: English
• ISSNs: 0960-1295

Abstract

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.