{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:15:09Z","timestamp":1759637709889},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1837,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that if <jats:italic>\u2131<\/jats:italic> is any \u201cwell-behaved\u201d subset of the Borel functions and we assume the Axiom of Determinacy then the hierarchy of degrees on <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200003716_inline1\" \/>(<jats:italic><jats:sup>\u03c9<\/jats:sup>\u03c9<\/jats:italic>) induced by <jats:italic>\u2131<\/jats:italic> turns out to look like the Wadge hierarchy (which is the special case where <jats:italic>\u2131<\/jats:italic> is the set of continuous functions).<\/jats:p>","DOI":"10.2178\/jsl\/1231082301","type":"journal-article","created":{"date-parts":[[2009,1,4]],"date-time":"2009-01-04T15:18:44Z","timestamp":1231082324000},"page":"27-49","source":"Crossref","is-referenced-by-count":16,"title":["Borel-amenable reducibilities for sets of reals"],"prefix":"10.1017","volume":"74","author":[{"given":"Luca Motto","family":"Ros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003716_ref016","unstructured":"Wadge W. W. , Reducibility and determinateness on the Baire space, Ph.D. thesis, University of California, Berkeley, 1983."},{"key":"S0022481200003716_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2006.05.008"},{"key":"S0022481200003716_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S0022481200003716_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0069298"},{"key":"S0022481200003716_ref004","doi-asserted-by":"publisher","DOI":"10.4064\/fm177-2-5"},{"key":"S0022481200003716_ref009","unstructured":"Ros L. Motto , A new characterization of Baire class 1 functions, To appear."},{"key":"S0022481200003716_ref008","unstructured":"Ros L. Motto , General Readabilities for Sets of Reals, Ph.D. thesis, Polytechnic of Turin, Italy, 2007."},{"key":"S0022481200003716_ref005","first-page":"1273","volume":"56","author":"Cicho\u0144","year":"1991","journal-title":"Decomposing Baire functions"},{"key":"S0022481200003716_ref006","first-page":"177","article-title":"First level Borel functions and isomorphisms","volume":"61","author":"Jayne","year":"1982","journal-title":"Journal de Mathematiques Pures et Appliqu\u00e9es"},{"key":"S0022481200003716_ref011","unstructured":"Ros L. Motto , Beyond Borel-amenability: scales and superamenable reductions, In preparation."},{"key":"S0022481200003716_ref012","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-98-00269-0"},{"key":"S0022481200003716_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(03)00022-8"},{"key":"S0022481200003716_ref010","unstructured":"Ros L. Motto , Baire reductions and good Borel reducihilities, In preparation."},{"key":"S0022481200003716_ref013","unstructured":"Steel J. R. , Determinateness and Subsystems of Analysis, Ph.D. thesis, University of California, Berkeley, 1977."},{"key":"S0022481200003716_ref003","unstructured":"Andretta A. , The SLO principle and the Wadge hierarchy, To appear."},{"key":"S0022481200003716_ref014","unstructured":"Van Wesep R. A. , Subsystems of Second-Order Arithmetic and Descriptive Set Theory under the Axiom of Determinateness, Ph.D. thesis, University of California, Berkeley, 1977."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003716","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T20:00:33Z","timestamp":1556654433000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003716\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,3]]}},"alternative-id":["S0022481200003716"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1231082301","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3]]}}}