{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T05:32:17Z","timestamp":1771651937945,"version":"3.50.1"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3479,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,9]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>A Turing degree a is said to be <jats:italic>almost everywhere dominating<\/jats:italic> if, for almost all <jats:italic>X<\/jats:italic> \u2208 2<jats:sup><jats:italic>\u03c9<\/jats:italic><\/jats:sup> with respect to the \u201cfair coin\u201d probability measure on 2<jats:sup><jats:italic>\u03c9<\/jats:italic><\/jats:sup>, and for all <jats:italic>g<\/jats:italic>: <jats:italic>\u03c9<\/jats:italic> \u2192 <jats:italic>\u03c9<\/jats:italic> Turing reducible to <jats:italic>X<\/jats:italic>, there exists <jats:italic>f<\/jats:italic>: <jats:italic>\u03c9<\/jats:italic> \u2192 <jats:italic>\u03c9<\/jats:italic> of Turing degree a which dominates <jats:italic>g<\/jats:italic>. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly defined classes of Turing degrees. We relate this problem to some questions in the reverse mathematics of measure theory.<\/jats:p>","DOI":"10.2178\/jsl\/1096901775","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:46:04Z","timestamp":1109799964000},"page":"914-922","source":"Crossref","is-referenced-by-count":20,"title":["Almost everywhere domination"],"prefix":"10.1017","volume":"69","author":[{"given":"Natasha L.","family":"Dobrinen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen G.","family":"Simpson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200007714_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/BF01621469"},{"key":"S0022481200007714_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(95)00042-9"},{"key":"S0022481200007714_ref015","doi-asserted-by":"crossref","unstructured":"Yu Xiaokang , Radon-Nikodym theorem is equivalent to arithmetical comprehension, in [9], 1990, pp. 289\u2013297.","DOI":"10.1090\/conm\/106\/1057829"},{"key":"S0022481200007714_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59971-2"},{"key":"S0022481200007714_ref009","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/106"},{"key":"S0022481200007714_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0253895-6"},{"key":"S0022481200007714_ref007","unstructured":"Martin Donald A. , Measure, category, and degrees of unsolvability, unpublished, typewritten, 16 pages, 1967."},{"key":"S0022481200007714_ref005","unstructured":"Kurtz Stuart A. , Randomness and genericity in the degrees of unsolvability, Ph.D. thesis , University of Illinois at Urbana-Champaign, 1981."},{"key":"S0022481200007714_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200007714_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/s001530100100"},{"key":"S0022481200007714_ref010","volume-title":"Reverse mathematics 2001","author":"Simpson","year":"2004"},{"key":"S0022481200007714_ref011","unstructured":"Simpson Stephen G. , sets and models of WKL0, in [10], preprint, 04 2000, 29 pages, to appear."},{"key":"S0022481200007714_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9440-2"},{"key":"S0022481200007714_ref004","unstructured":"Kautz Steven M. , Degrees of random sets, Ph.D. thesis , Cornell University, 1991."},{"key":"S0022481200007714_ref014","unstructured":"Yu Xiaokang , Measure theory in weak subsystems of second order arithmetic, Ph.D. thesis , Pennsylvania State University, 1987."},{"key":"S0022481200007714_ref017","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19940400102"},{"key":"S0022481200007714_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90232-3"},{"key":"S0022481200007714_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12898-5"},{"key":"S0022481200007714_ref006","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19660120125"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200007714","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T20:26:48Z","timestamp":1557174408000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200007714\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,9]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2004,9]]}},"alternative-id":["S0022481200007714"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1096901775","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,9]]}}}