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DC Field | Value | Language |
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dc.contributor.author | Gregoriades, Vassillos | en_US |
dc.contributor.author | Kihara, Takayuki | en_US |
dc.contributor.author | Ng, Meng Keng | en_US |
dc.date.accessioned | 2022-02-11T06:57:37Z | - |
dc.date.available | 2022-02-11T06:57:37Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | 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 | en_US |
dc.identifier.issn | 0219-0613 | en_US |
dc.identifier.uri | https://hdl.handle.net/10356/155095 | - |
dc.description.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. | en_US |
dc.language.iso | en | en_US |
dc.relation | MOE2015-T2-2-05 | en_US |
dc.relation | MOE-RG26/13 | en_US |
dc.relation.ispartof | Journal of Mathematical Logic | en_US |
dc.rights | © 2021 World Scientific Publishing Company. All rights reserved. | en_US |
dc.subject | Science::Mathematics | en_US |
dc.title | Turing degrees in Polish spaces and decomposability of Borel functions | en_US |
dc.type | Journal Article | en |
dc.contributor.school | School of Physical and Mathematical Sciences | en_US |
dc.identifier.doi | 10.1142/S021906132050021X | - |
dc.identifier.scopus | 2-s2.0-85086251207 | - |
dc.identifier.issue | 1 | en_US |
dc.identifier.volume | 21 | en_US |
dc.identifier.spage | 2050021 | en_US |
dc.subject.keywords | Countably Continuous Function | en_US |
dc.subject.keywords | Jayne–Rogers Theorem | en_US |
dc.description.acknowledgement | V. Gregoriades was partially supported by the E. U. Project No: 294962 COM-PUTAL. The second named author was partially supported by a Grant-in-Aidfor JSPS fellows and the JSPS Core-to-Core Program (A. Advanced Research Net-works). The third author was partially supported by the grants MOE-RG26/13 andMOE2015-T2-2-055. | en_US |
item.fulltext | No Fulltext | - |
item.grantfulltext | none | - |
Appears in Collections: | SPMS Journal Articles |
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