Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/159280
Title: Computability of Polish spaces up to homeomorphism
Authors: Harrison-Trainor, Matthew
Melnikov, Alexander
Ng, Keng Meng
Keywords: Science::Mathematics
Issue Date: 2020
Source: Harrison-Trainor, M., Melnikov, A. & Ng, K. M. (2020). Computability of Polish spaces up to homeomorphism. Journal of Symbolic Logic, 85(4), 1664-1686. https://dx.doi.org/10.1017/jsl.2020.67
Journal: Journal of Symbolic Logic
Abstract: We study computable Polish spaces and Polish groups up to homeomorphism. We prove a natural effective analogy of Stone duality, and we also develop an effective definability technique which works up to homeomorphism. As an application, we show that there is a Polish space not homeomorphic to a computable one. We apply our techniques to build, for any computable ordinal, an effectively closed set not homeomorphic to any -computable Polish space; this answers a question of Nies. We also prove analogous results for compact Polish groups and locally path-connected spaces.
URI: https://hdl.handle.net/10356/159280
ISSN: 0022-4812
DOI: 10.1017/jsl.2020.67
Rights: © 2020 The Association for Symbolic Logic. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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