Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/155095
Title: Turing degrees in Polish spaces and decomposability of Borel functions
Authors: Gregoriades, Vassillos
Kihara, Takayuki
Ng, Meng Keng
Keywords: Science::Mathematics
Issue Date: 2021
Source: Gregoriades, V., Kihara, T. & Ng, M. K. (2021). Turing degrees in Polish spaces and decomposability of Borel functions. Journal of Mathematical Logic, 21(1), 2050021-. https://dx.doi.org/10.1142/S021906132050021X
Project: MOE2015-T2-2-05
MOE-RG26/13
Journal: Journal of Mathematical Logic
Abstract: We give a partial answer to an important open problem in descriptive set theory, the Decomposability Conjecture for Borel functions on an analytic subset of a Polish space to a separable metrizable space. Our techniques employ deep results from effective descriptive set theory and recursion theory. In fact it is essential to extend several prominent results in recursion theory (e.g. the Shore-Slaman Join Theorem) to the setting of Polish spaces. As a by-product we give both positive and negative results on the Martin Conjecture on the degree preserving Borel functions between Polish spaces. Additionally we prove results about the transfinite version as well as the computable version of the Decomposability Conjecture.
URI: https://hdl.handle.net/10356/155095
ISSN: 0219-0613
DOI: 10.1142/S021906132050021X
Rights: © 2021 World Scientific Publishing Company. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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