{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T02:27:01Z","timestamp":1648520821859},"reference-count":36,"publisher":"EDP Sciences","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Theor. Inf. Appl."],"published-print":{"date-parts":[[2007,1]]},"DOI":"10.1051\/ita:2007008","type":"journal-article","created":{"date-parts":[[2007,4,23]],"date-time":"2007-04-23T10:56:28Z","timestamp":1177325788000},"page":"3-25","source":"Crossref","is-referenced-by-count":0,"title":["On the hierarchies of \u0394<sub>2<\/sub><sup>0<\/sup>-real numbers"],"prefix":"10.1051","volume":"41","author":[{"given":"Xizhong","family":"Zheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2007,4,24]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1006\/jcom.2000.0561","volume":"16","author":"Ambos-Spies","year":"2000","journal-title":"J. Complexity"},{"key":"R2","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0304-3975(99)00159-0","volume":"255","author":"Calude","year":"2001","journal-title":"Theor. Comput. Sci."},{"key":"R3","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1002\/malq.200310103","volume":"50","author":"Downey","year":"2004","journal-title":"Math. Logic Quart."},{"key":"R4","first-page":"97","volume":"18","author":"Downey","year":"2005","journal-title":"Lect. Notes Log."},{"key":"R5","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1007\/3-540-45335-0_2","volume":"2064","author":"Dunlop","year":"2001","journal-title":"Lect. Notes Comput. Sci."},{"key":"R6","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1090\/S0002-9939-1954-0063328-5","volume":"5","author":"Gordon Rice","year":"1954","journal-title":"Proc. Amer. Math. Soc."},{"key":"R7","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0304-3975(98)00098-X","volume":"210","author":"Relatively","year":"1999","journal-title":"Theor. Comput. Sci."},{"key":"R8","unstructured":"K.-I. Ko,Complexity Theory of Real Functions. Progress in Theoretical Computer Science. Birkh\u00e4user, Boston, MA (1991)."},{"key":"R9","first-page":"47","volume":"7","author":"Leonidovich Ershov","year":"1968","journal-title":"Algebra i Logika"},{"key":"R10","doi-asserted-by":"crossref","first-page":"7","DOI":"10.2307\/2266321","volume":"18","author":"Myhill","year":"1953","journal-title":"J. Symbolic Logic"},{"key":"R11","unstructured":"K. Meng Ng, M. Sc. Thesis. National University of Singapore. (In preparation)."},{"key":"R12","unstructured":"P. Odifreddi,Classical recursion theory,Studies in Logic and the Foundations of Mathematics125. North-Holland Publishing Co., Amsterdam (1989)."},{"key":"R13","unstructured":"P. Odifreddi,Classical recursion theory. Vol. II,Studies in Logic and the Foundations of Mathematics143. North-Holland Publishing Co., Amsterdam (1999)."},{"key":"R14","unstructured":"A. Raichev, D.c.e. reals, relative randomness, and real closed fields, inCCA 2004, August 16\u201320, 2004, Lutherstadt Wittenberg, Germany(2004)."},{"key":"R15","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1016\/S0885-064X(03)00066-9","volume":"19","author":"Rettinger","year":"2003","journal-title":"J. Complexity"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"R. Rettinger and X. Zheng, Solovay reducibility on d-c.e. real numbers, inCOCOON 2005, August 16\u201319, 2005, Kunming, China.Lect. Notes Comput. Sci.(2005) 359\u2013368.","DOI":"10.1007\/11533719_37"},{"key":"R17","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1007\/3-540-44679-6_65","volume":"2108","author":"Rettinger","year":"2001","journal-title":"Lect. Notes Comput. Sci."},{"key":"R18","first-page":"280","volume":"16","author":"Robinson","year":"1951","journal-title":"J. Symbolic Logic"},{"key":"R19","doi-asserted-by":"crossref","first-page":"284","DOI":"10.2307\/420992","volume":"2","author":"Soare","year":"1996","journal-title":"Bull. Symbolic Logic"},{"key":"R20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.2140\/pjm.1969.31.215","volume":"31","author":"Soare","year":"1969","journal-title":"Pacific J. Math."},{"key":"R21","first-page":"271","volume":"140","author":"Soare","year":"1969","journal-title":"Trans.\u2000Amer.\u2000Math.\u2000Soc."},{"key":"R22","doi-asserted-by":"crossref","unstructured":"R.I. Soare, Recursively enumerable sets and degrees. A study of computable functions and computably generated sets, inPerspectives in Mathematical Logic. Springer-Verlag, Berlin (1987).","DOI":"10.1007\/978-3-662-02460-7"},{"key":"R23","unstructured":"R.M. Solovay, Draft of a paper (or a series of papers) on chaitin's work .... manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY (1975) 215."},{"key":"R24","doi-asserted-by":"crossref","first-page":"145","DOI":"10.2307\/2267043","volume":"14","author":"Specker","year":"1949","journal-title":"J. Symbolic Logic"},{"key":"R25","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1112\/plms\/s2-42.1.230","volume":"42","author":"Turing","year":"1936","journal-title":"Proceedings of the London Mathematical Society"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"A.M. Turing, On computable numbers, with an application to the \u201cEntscheidungsproblem\u201d. A correction, inproceedings of the London Mathematical Society43(1937) 544\u2013546.","DOI":"10.1112\/plms\/s2-43.6.544"},{"key":"R27","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1007\/BFb0055831","volume":"1450","author":"Weihrauch","year":"1998","journal-title":"Lect. Notes Comput. Sci."},{"key":"R28","unstructured":"G. Wu, Regular reals, inProceedings of CCA 2003, Cincinnati, USA, edited by V. Brattka, M. Schr\u00f6der, K. Weihrauch and N. Zhong, volume 302 - 8\/2003 ofInformatik Berichte, FernUniversit\u00e4t Hagen(2003) 363\u2013374."},{"key":"R29","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1002\/1521-3870(200210)48:1+<131::AID-MALQ131>3.0.CO;2-#","volume":"48","author":"Zheng","year":"2002","journal-title":"Mathematical Logic Quarterly"},{"key":"R30","unstructured":"X. Zheng, On the divergence bounded computable real numbers, inComputing and Combinatorics, edited by T. Warnow and B. Zhu.Lect. Notes Comput. Sci.2697102\u2013111, Berlin (2003). Springer. COOCON 2003, July 25\u201328, 2003, Big Sky, MT, USA."},{"key":"R31","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1093\/logcom\/13.2.159","volume":"13","author":"Zheng","year":"2003","journal-title":"J. Logic Computation"},{"key":"R32","unstructured":"X. Zheng and R. Rettinger, A note on the Turing degree of divergence bounded computable real numbers, inCCA 2004, August 16\u201320, Lutherstadt Wittenberg, Germany(2004)."},{"key":"R33","unstructured":"X. Zheng and R. Rettinger, On the extensions of solovay reducibility, inCOOCON 2004, August 17\u201320, Jeju Island, Korea.Lect. Notes Comput. Sci.3106(2004)."},{"key":"R34","doi-asserted-by":"crossref","unstructured":"X. Zheng and R. Rettinger, Weak computability and representation of reals.Mathematical Logic Quarterly50(4\/5) (2004) 431\u2013442.","DOI":"10.1002\/malq.200310110"},{"key":"R35","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s00224-004-1193-z","volume":"38","author":"Zheng","year":"2005","journal-title":"Theor. Comput. Syst."},{"key":"R36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/malq.200410016","volume":"51","author":"Zheng","year":"2005","journal-title":"Mathematical Logic Quarterly"}],"container-title":["RAIRO - Theoretical Informatics and Applications"],"original-title":[],"link":[{"URL":"http:\/\/www.rairo-ita.org\/10.1051\/ita:2007008\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T08:50:12Z","timestamp":1556355012000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rairo-ita.org\/10.1051\/ita:2007008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1]]},"references-count":36,"journal-issue":{"issue":"1"},"alternative-id":["ita06010"],"URL":"https:\/\/doi.org\/10.1051\/ita:2007008","relation":{},"ISSN":["0988-3754","1290-385X"],"issn-type":[{"value":"0988-3754","type":"print"},{"value":"1290-385X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1]]}}}