Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/155095
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dc.contributor.authorGregoriades, Vassillosen_US
dc.contributor.authorKihara, Takayukien_US
dc.contributor.authorNg, Meng Kengen_US
dc.date.accessioned2022-02-11T06:57:37Z-
dc.date.available2022-02-11T06:57:37Z-
dc.date.issued2021-
dc.identifier.citationGregoriades, 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/S021906132050021Xen_US
dc.identifier.issn0219-0613en_US
dc.identifier.urihttps://hdl.handle.net/10356/155095-
dc.description.abstractWe 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.isoenen_US
dc.relationMOE2015-T2-2-05en_US
dc.relationMOE-RG26/13en_US
dc.relation.ispartofJournal of Mathematical Logicen_US
dc.rights© 2021 World Scientific Publishing Company. All rights reserved.en_US
dc.subjectScience::Mathematicsen_US
dc.titleTuring degrees in Polish spaces and decomposability of Borel functionsen_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.identifier.doi10.1142/S021906132050021X-
dc.identifier.scopus2-s2.0-85086251207-
dc.identifier.issue1en_US
dc.identifier.volume21en_US
dc.identifier.spage2050021en_US
dc.subject.keywordsCountably Continuous Functionen_US
dc.subject.keywordsJayne–Rogers Theoremen_US
dc.description.acknowledgementV. 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.grantfulltextnone-
item.fulltextNo Fulltext-
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