{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T02:25:10Z","timestamp":1768703110471,"version":"3.49.0"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2014,9,13]],"date-time":"2014-09-13T00:00:00Z","timestamp":1410566400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2015,2]]},"DOI":"10.1007\/s00153-014-0402-y","type":"journal-article","created":{"date-parts":[[2014,9,12]],"date-time":"2014-09-12T04:07:28Z","timestamp":1410494848000},"page":"59-73","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Friedberg numberings in the Ershov hierarchy"],"prefix":"10.1007","volume":"54","author":[{"given":"Serikzhan A.","family":"Badaev","sequence":"first","affiliation":[]},{"given":"Mustafa","family":"Manat","sequence":"additional","affiliation":[]},{"given":"Andrea","family":"Sorbi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,9,13]]},"reference":[{"key":"402_CR1","unstructured":"Ash, C.J., Knight, J.: Computable Structures and the Hyperarithmetical Hierarchy, volume 144 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam (2000)"},{"key":"402_CR2","doi-asserted-by":"crossref","unstructured":"Badaev, S.A., Goncharov, S.S.: On computable minimal enumerations. In: Yu, L. Ershov, E.I. Khukhro, V.M. Levchuk, Podufalov, N.D. (eds.) Algebra. Proceedings of the Third International Conference on Algebra Held in Krasnoyarsk, August 23\u201328, 1993, De Gruyter Proceedings in Mathematics, pp. 21\u201332. Walter de Gruyter, Berlin (1996)","DOI":"10.1515\/9783110813418-005"},{"issue":"5","key":"402_CR3","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1007\/BF01040653","volume":"8","author":"Y.L. Ershov","year":"1967","unstructured":"Ershov Y.L.: Enumerations of families of general recursive functions. Sib. Math. J. 8(5), 771\u2013778 (1967)","journal-title":"Sib. Math. J."},{"key":"402_CR4","doi-asserted-by":"crossref","unstructured":"Ershov, Y.L.: A hierarchy of sets, I. Algebra Logic, 7(1), 25\u201343 (1968) Russian","DOI":"10.1007\/BF02218750"},{"issue":"4","key":"402_CR5","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1007\/BF02218664","volume":"7","author":"Y.L. Ershov","year":"1968","unstructured":"Ershov Y.L.: A hierarchy of sets, II. Algebra Log. 7(4), 212\u2013232 (1968)","journal-title":"Algebra Log."},{"issue":"1","key":"402_CR6","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/BF02219847","volume":"9","author":"Y.L. Ershov","year":"1970","unstructured":"Ershov Y.L.: A hierarchy of sets, III. Algebra Log. 9(1), 20\u201331 (1970)","journal-title":"Algebra Log."},{"key":"402_CR7","unstructured":"Ershov, Y.L.: Theory of Numberings. Nauka, Moscow (1977) Russian"},{"key":"402_CR8","doi-asserted-by":"crossref","unstructured":"Ershov, Y.L.: Theory of numberings. In: Griffor, E.R. (ed.) Handbook of Computability Theory, volume 140 of Studies in Logic and the Foundations of Mathematics, pp. 473\u2013506. Elsevier Science, Amsterdam (1999)","DOI":"10.1016\/S0049-237X(99)80030-5"},{"key":"402_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-4305-3","volume-title":"Constructive Models. Siberian School of Algebra and Logic","author":"Y.L. Ershov","year":"2000","unstructured":"Ershov Y.L., Goncharov S.S.: Constructive Models. Siberian School of Algebra and Logic. Springer, Berlin (2000)"},{"key":"402_CR10","doi-asserted-by":"crossref","first-page":"309","DOI":"10.2307\/2964290","volume":"23","author":"R.M. Friedberg","year":"1958","unstructured":"Friedberg R.M.: Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication. J. Symb. Log. 23, 309\u2013316 (1958)","journal-title":"J. Symb. Log."},{"issue":"6","key":"402_CR11","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/BF02671553","volume":"36","author":"S.S. Goncharov","year":"1997","unstructured":"Goncharov S.S., Sorbi A.: Generalized computable numerations and non-trivial Rogers semilattices. Algebra Log. 36(6), 359\u2013369 (1997)","journal-title":"Algebra Log."},{"issue":"5","key":"402_CR12","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF01669607","volume":"19","author":"S.S. Goncharov","year":"1980","unstructured":"Goncharov S.S.: Computable single-valued numerations. Algebra Log. 19(5), 325\u2013356 (1980)","journal-title":"Algebra Log."},{"issue":"6","key":"402_CR13","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/BF01669323","volume":"19","author":"S.S. Goncharov","year":"1980","unstructured":"Goncharov S.S.: Problem of the number of non-self-equivalent constructivizations. Algebra Log. 19(6), 401\u2013414 (1980)","journal-title":"Algebra Log."},{"key":"402_CR14","unstructured":"Goncharov, S.S.: The family with unique univalent but not the smallest enumeration. In: Trudy Inst. Matem. SO AN SSSR, Nauka, Novosibirsk, vol. 8, pp. 42\u201348 (1988) Russian"},{"issue":"2","key":"402_CR15","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1023\/A:1015352513117","volume":"41","author":"S.S. Goncharov","year":"2002","unstructured":"Goncharov S.S., Lempp S., Solomon D.R.: Friedberg numberings of families of n-computably enumerable sets. Algebra Log. 41(2), 81\u201386 (2002)","journal-title":"Algebra Log."},{"issue":"4","key":"402_CR16","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF01792984","volume":"30","author":"M. Kummer","year":"1990","unstructured":"Kummer M.: Some applications of computable one-one numberings. Arch. Math. Log. 30(4), 219\u2013230 (1990)","journal-title":"Arch. Math. Log."},{"key":"402_CR17","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0020-0190(95)00036-C","volume":"54","author":"M. Kummer","year":"1995","unstructured":"Kummer M.: A learning-theoretic characterization of classes of recursive functions. Inf. Process. Lett. 54, 205\u2013211 (1995)","journal-title":"Inf. Process. Lett."},{"issue":"6","key":"402_CR18","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1007\/s10469-012-9162-0","volume":"50","author":"M. Manat","year":"2012","unstructured":"Manat M., Sorbi A.: Positive undecidable numberings in the Ershov hierarchy. Algebra Log. 50(6), 512\u2013525 (2012)","journal-title":"Algebra Log."},{"key":"402_CR19","unstructured":"Ospichev, S.: Computable family of $${\\Sigma^{-1}_a}$$ \u03a3 a - 1 -sets without Friedberg numberings. In: Ferreira, F., Guerra, H., Mayordomo, E., Rasga, J. (eds.) 6th Conference on Computability in Europe, CiE 2010, Ponta Delgada, Azores, Portugal, June\/July 2010. Abstract and Handout Booklet, pp. 311\u2013315. Centre for Applied Mathematics and Information Technology, Department of Mathematics, University of Azores (2010)"},{"key":"402_CR20","volume-title":"Theory of Recursive Functions and Effective Computability","author":"H. Rogers Jr.","year":"1967","unstructured":"Rogers H. Jr.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)"},{"issue":"6","key":"402_CR21","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1023\/B:ALLO.0000004175.64588.32","volume":"42","author":"Z.T. Talasbaeva","year":"2003","unstructured":"Talasbaeva Z.T.: Positive numberings of families of sets in the Ershov hierarchy. Algebra Log. 42(6), 413\u2013418 (2003)","journal-title":"Algebra Log."}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-014-0402-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-014-0402-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-014-0402-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,14]],"date-time":"2019-08-14T22:42:53Z","timestamp":1565822573000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-014-0402-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,13]]},"references-count":21,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["402"],"URL":"https:\/\/doi.org\/10.1007\/s00153-014-0402-y","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,13]]}}}