{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T23:37:56Z","timestamp":1719963476879},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2021,8,12]],"date-time":"2021-08-12T00:00:00Z","timestamp":1628726400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2021,12]]},"abstract":"Abstract<\/jats:title>The \n$\\Omega $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> numbers\u2014the halting probabilities of universal prefix-free machines\u2014are known to be exactly the Martin-L\u00f6f random left-c.e. reals. We show that one cannot uniformly produce, from a Martin-L\u00f6f random left-c.e. real \n$\\alpha $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, a universal prefix-free machine U<\/jats:italic> whose halting probability is \n$\\alpha $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We also answer a question of Barmpalias and Lewis-Pye by showing that given a left-c.e. real \n$\\alpha $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, one cannot uniformly produce a left-c.e. real \n$\\beta $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that \n$\\alpha - \\beta $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is neither left-c.e. nor right-c.e.<\/jats:p>","DOI":"10.1017\/jsl.2021.58","type":"journal-article","created":{"date-parts":[[2021,8,12]],"date-time":"2021-08-12T02:55:01Z","timestamp":1628736901000},"page":"1612-1631","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["SOME QUESTIONS OF UNIFORMITY IN ALGORITHMIC RANDOMNESS"],"prefix":"10.1017","volume":"86","author":[{"given":"LAURENT","family":"BIENVENU","sequence":"first","affiliation":[]},{"given":"BARBARA F.","family":"CSIMA","sequence":"additional","affiliation":[]},{"given":"MATTHEW","family":"HARRISON-TRAINOR","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,8,12]]},"reference":[{"key":"S002248122100058X_r10","doi-asserted-by":"publisher","DOI":"10.1145\/321892.321894"},{"key":"S002248122100058X_r4","unstructured":"[4] Bienvenu, L. and Downey, R. , Kolmogorov complexity and Solovay functions, Symposium on Theoretical Aspects of Computer Science (STACS 2009), Dagstuhl Seminar Proceedings, 09001, Schloss Dagstuhl\u2014Leibniz-Zentrum fuer Informatik, Germany Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, 2009, pp. 147\u2013158."},{"key":"S002248122100058X_r16","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199230761.001.0001"},{"key":"S002248122100058X_r5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2015.04.004"},{"key":"S002248122100058X_r9","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129508007238"},{"key":"S002248122100058X_r14","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539799357441"},{"key":"S002248122100058X_r3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-50062-1_37"},{"key":"S002248122100058X_r2","first-page":"623","volume-title":"Algorithmic Randomness: Progress and Prospects","author":"Barmpalias","year":"2018"},{"key":"S002248122100058X_r12","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539700376937"},{"key":"S002248122100058X_r18","first-page":"215","volume-title":"Handwritten Manuscript Related to Chaitin\u2019s Work","author":"Solovay","year":"1975"},{"key":"S002248122100058X_r7","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(99)00159-0"},{"key":"S002248122100058X_r11","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68441-3"},{"key":"S002248122100058X_r15","unstructured":"[15] Ng, K. M. , Some properties of d.c.e. reals and their degrees , Master\u2019s thesis, National University of Singapore, 2006."},{"key":"S002248122100058X_r8","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2011.01.002"},{"key":"S002248122100058X_r6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-27654-5_3"},{"key":"S002248122100058X_r1","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.2000.0561"},{"key":"S002248122100058X_r13","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2008.12.009"},{"key":"S002248122100058X_r17","first-page":"319","article-title":"Relative randomness and real closed fields","volume":"70","author":"Raichev","year":"2005","journal-title":"Journal"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248122100058X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T03:32:48Z","timestamp":1641958368000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248122100058X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,12]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["S002248122100058X"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2021.58","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,12]]},"assertion":[{"value":"\u00a9 Association for Symbolic Logic 2021","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}