{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T00:47:59Z","timestamp":1694652479168},"reference-count":20,"publisher":"Elsevier BV","issue":"5","license":[{"start":{"date-parts":[[2003,10,1]],"date-time":"2003-10-01T00:00:00Z","timestamp":1064966400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":3577,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Complexity"],"published-print":{"date-parts":[[2003,10]]},"DOI":"10.1016\/s0885-064x(03)00066-9","type":"journal-article","created":{"date-parts":[[2003,9,12]],"date-time":"2003-09-12T06:44:21Z","timestamp":1063349061000},"page":"672-691","source":"Crossref","is-referenced-by-count":7,"title":["On the hierarchy and extension of monotonically computable real numbers"],"prefix":"10.1016","volume":"19","author":[{"given":"Robert","family":"Rettinger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xizhong","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/S0885-064X(03)00066-9_BIB1","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1006\/jcom.2000.0561","article-title":"Weakly computable real numbers","volume":"16","author":"Ambos-Spies","year":"2000","journal-title":"J. Complexity"},{"key":"10.1016\/S0885-064X(03)00066-9_BIB2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0304-3975(01)00027-5","article-title":"A characterization of c.e. random reals","volume":"271","author":"Calude","year":"2002","journal-title":"Theoret. Comput. Sci."},{"issue":"2","key":"10.1016\/S0885-064X(03)00066-9_BIB3","doi-asserted-by":"crossref","first-page":"105","DOI":"10.3233\/FI-1998-33201","article-title":"Computable approximations of reals","volume":"33","author":"Calude","year":"1998","journal-title":"Fundamenta Informat."},{"key":"10.1016\/S0885-064X(03)00066-9_BIB4","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0304-3975(99)00159-0","article-title":"Recursively enumerable reals and Chaitin \u03a9 numbers","volume":"255","author":"Calude","year":"2001","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0885-064X(03)00066-9_BIB5","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1145\/321892.321894","article-title":"A theory of program size formally identical to information theory","volume":"22","author":"Chaitin","year":"1975","journal-title":"J. ACM"},{"issue":"1","key":"10.1016\/S0885-064X(03)00066-9_BIB6","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1137\/S0097539799357441","article-title":"Randomness and recursive enumerability","volume":"31","author":"Ku\u00e7era","year":"2001","journal-title":"SIAM J. Comput."},{"key":"10.1016\/S0885-064X(03)00066-9_BIB7","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1016\/S0019-9958(66)80018-9","article-title":"The definition of random sequences","volume":"9","author":"Martin-L\u00f6f","year":"1966","journal-title":"Inform. Control"},{"key":"10.1016\/S0885-064X(03)00066-9_BIB8","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0003-4843(79)90021-4","article-title":"A computable ordinary differential equation which possesses no computable solution","volume":"17","author":"Pour-El","year":"1979","journal-title":"Ann. Math. Logic"},{"issue":"3","key":"10.1016\/S0885-064X(03)00066-9_BIB9","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1002\/1521-3870(200204)48:3<459::AID-MALQ459>3.0.CO;2-9","article-title":"Monotonically computable real numbers","volume":"48","author":"Rettinger","year":"2002","journal-title":"Math. Log. Quart."},{"key":"10.1016\/S0885-064X(03)00066-9_BIB10","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1090\/S0002-9939-1954-0063328-5","article-title":"Recursive real numbers","volume":"5","author":"Rice","year":"1954","journal-title":"Proc. Amer. Math. Soc."},{"key":"10.1016\/S0885-064X(03)00066-9_BIB11","first-page":"280","article-title":"Review of \u201cPeter, R., Rekursive Funktionen\u201d","volume":"16","author":"Robinson","year":"1951","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S0885-064X(03)00066-9_BIB12","doi-asserted-by":"crossref","first-page":"215","DOI":"10.2140\/pjm.1969.31.215","article-title":"Cohesive sets and recursively enumerable Dedekind cuts","volume":"31","author":"Soare","year":"1969","journal-title":"Pacific J. Math."},{"key":"10.1016\/S0885-064X(03)00066-9_BIB13","first-page":"271","article-title":"Recursion theory and Dedekind cuts","volume":"140","author":"Soare","year":"1969","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/S0885-064X(03)00066-9_BIB14","unstructured":"R.M. Solovay, Draft of a paper (or a series of papers) on chaitin's work\u2026 manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1975, p. 215."},{"issue":"3","key":"10.1016\/S0885-064X(03)00066-9_BIB15","doi-asserted-by":"crossref","first-page":"145","DOI":"10.2307\/2267043","article-title":"Nicht konstruktiv beweisbare S\u00e4tze der Analysis","volume":"14","author":"Specker","year":"1949","journal-title":"J. Symbolic Logic"},{"issue":"2","key":"10.1016\/S0885-064X(03)00066-9_BIB16","first-page":"230","article-title":"On computable numbers, with an application to the \u201cEntscheidungsproblem\u201d","volume":"42","author":"Turing","year":"1936","journal-title":"Proc. London Math. Soc."},{"key":"10.1016\/S0885-064X(03)00066-9_BIB17","series-title":"Computable Analysis, An Introduction","author":"Weihrauch","year":"2000"},{"key":"10.1016\/S0885-064X(03)00066-9_BIB18","doi-asserted-by":"crossref","unstructured":"K. Weihrauch, X. Zheng, A finite hierarchy of the recursively enumerable real numbers, in: Proceedings of MFCS\u201998, Brno, Czech Republic, August, 1998, Lecture Notes in Computer Science, Vol. 1450, Springer, Berlin, 1998, pp. 798\u2013806.","DOI":"10.1007\/BFb0055831"},{"issue":"2","key":"10.1016\/S0885-064X(03)00066-9_BIB19","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/S0304-3975(01)00107-4","article-title":"Closure properties on real numbers under limits and computable operators","volume":"284","author":"Zheng","year":"2002","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0885-064X(03)00066-9_BIB20","doi-asserted-by":"crossref","unstructured":"R. Rettinger, X. Zheng, Hierarchy of monotonically computable real numbers, in: Proceedings of MFCS\u201901, Mari\u00e1nsk\u00e9 L\u00e1zn\u011b, Czech Republic, August 27\u201331, 2001, Lecture Notes in Computer Science, Vol. 2136, Springer, Berlin, 2001, pp. 633\u2013644.","DOI":"10.1007\/3-540-44683-4_55"}],"container-title":["Journal of Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0885064X03000669?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0885064X03000669?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,3,25]],"date-time":"2020-03-25T14:09:17Z","timestamp":1585145357000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0885064X03000669"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,10]]},"references-count":20,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2003,10]]}},"alternative-id":["S0885064X03000669"],"URL":"https:\/\/doi.org\/10.1016\/s0885-064x(03)00066-9","relation":{},"ISSN":["0885-064X"],"issn-type":[{"value":"0885-064X","type":"print"}],"subject":[],"published":{"date-parts":[[2003,10]]}}}