{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T20:42:40Z","timestamp":1761943360406,"version":"build-2065373602"},"publisher-location":"Berlin, Heidelberg","reference-count":12,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540648277"},{"type":"electronic","value":"9783540685326"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1998]]},"DOI":"10.1007\/bfb0055831","type":"book-chapter","created":{"date-parts":[[2006,8,17]],"date-time":"2006-08-17T17:36:31Z","timestamp":1155836191000},"page":"798-806","source":"Crossref","is-referenced-by-count":13,"title":["A finite hierarchy of the recursively enumerable real numbers"],"prefix":"10.1007","author":[{"given":"Klaus","family":"Weihrauch","sequence":"first","affiliation":[]},{"given":"Xizhong","family":"Zheng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,5,28]]},"reference":[{"key":"78_CR1","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BF01744572","volume":"16","author":"K. Ko","year":"1983","unstructured":"Ker-I Ko On the definitions of some complexity classes of real numbers, Math. Systems Theory 16(1983) 95\u2013100.","journal-title":"Math. Systems Theory"},{"key":"78_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/2271331","volume":"28","author":"A. H. Lachlan","year":"1963","unstructured":"A. H. Lachlan Recursive real numbers. J. Symbolic Logic 28(1963), 1\u201316.","journal-title":"J. Symbolic Logic"},{"key":"78_CR3","doi-asserted-by":"publisher","first-page":"7","DOI":"10.2307\/2266321","volume":"18","author":"J. Myhill","year":"1953","unstructured":"J. Myhill Criteria of constructivity for real numbers, J. Symbolic Logic 18(1953), 7\u201310.","journal-title":"J. Symbolic Logic"},{"key":"78_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-21717-7","volume-title":"Computability in Analysis and Physics","author":"M. Pour-El","year":"1989","unstructured":"M. Pour-El & J. Richards Computability in Analysis and Physics. Springer-Verlag, Berlin, Heidelberg, 1989."},{"key":"78_CR5","doi-asserted-by":"publisher","first-page":"784","DOI":"10.2307\/2031867","volume":"5","author":"H. G. Rice","year":"1954","unstructured":"H. G. Rice Recursive real numbers, Proc. Amer. Math. Soc. 5(1954), 784\u2013791.","journal-title":"Proc. Amer. Math. Soc."},{"key":"78_CR6","doi-asserted-by":"publisher","first-page":"280","DOI":"10.2307\/2267933","volume":"16","author":"R. M. Robinson","year":"1951","unstructured":"R. M. Robinson Review of \u201cR. Peter: \u2018Rekursive Funktionen', Akad. Kiado. Budapest, 1951\u201d, J. Symb. Logic 16(1951), 280.","journal-title":"J. Symb. Logic"},{"key":"78_CR7","volume-title":"Theory of Recursive Functions and Effective Computability","author":"H. Rogers Jr.","year":"1967","unstructured":"H. Jr. Rogers Theory of Recursive Functions and Effective Computability McGraw-Hill, Inc. New York, 1967."},{"key":"78_CR8","doi-asserted-by":"publisher","first-page":"271","DOI":"10.2307\/1995137","volume":"140","author":"R. Soare","year":"1969","unstructured":"R. Soare Recursion theory and Dedekind cuts, Trans, Amer. Math. Soc. 140(1969), 271\u2013294.","journal-title":"Trans, Amer. Math. Soc."},{"issue":"no.1","key":"78_CR9","doi-asserted-by":"crossref","first-page":"215","DOI":"10.2140\/pjm.1969.31.215","volume":"31","author":"R. Soare","year":"1969","unstructured":"R. Soare Cohensive sets and recursive enumerable Dedekind cuts Pacific J. of Math. 31(1969), no.1, 215\u2013231.","journal-title":"Pacific J. of Math."},{"key":"78_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02460-7","volume-title":"Recursively Enumerable Sets and Degrees","author":"R. Soare","year":"1987","unstructured":"R. Soare Recursively Enumerable Sets and Degrees, Springer-Verlag, Berlin, Heidelberg, 1987."},{"key":"78_CR11","doi-asserted-by":"publisher","first-page":"145","DOI":"10.2307\/2267043","volume":"14","author":"E. Specter","year":"1949","unstructured":"E. Specter Nicht konstruktive beweisbare S\u00e4tze der Analysis, J. Symbolic Logic 14(1949), 145\u2013158","journal-title":"J. Symbolic Logic"},{"key":"78_CR12","volume-title":"EATCS Monographs on Theoretical Computer Science Vol. 9","author":"K. Weihrauch","year":"1987","unstructured":"K. Weihrauch Computability. EATCS Monographs on Theoretical Computer Science Vol. 9, Springer-Verlag, Berlin, Heidelberg, 1987."}],"container-title":["Lecture Notes in Computer Science","Mathematical Foundations of Computer Science 1998"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0055831","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,11]],"date-time":"2019-02-11T23:22:32Z","timestamp":1549927352000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0055831"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"ISBN":["9783540648277","9783540685326"],"references-count":12,"URL":"https:\/\/doi.org\/10.1007\/bfb0055831","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1998]]}}}