{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:08:33Z","timestamp":1759147713283,"version":"3.40.3"},"publisher-location":"Cham","reference-count":36,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319500614"},{"type":"electronic","value":"9783319500621"}],"license":[{"start":{"date-parts":[[2016,12,1]],"date-time":"2016-12-01T00:00:00Z","timestamp":1480550400000},"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":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-50062-1_27","type":"book-chapter","created":{"date-parts":[[2016,11,30]],"date-time":"2016-11-30T10:09:42Z","timestamp":1480500582000},"page":"469-478","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Survey of Results on the d-c.e. and n-c.e. Degrees"],"prefix":"10.1007","author":[{"given":"Marat M.","family":"Arslanov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Iskander Sh.","family":"Kalimullin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,12,1]]},"reference":[{"key":"27_CR1","first-page":"270","volume":"283","author":"MM Arslanov","year":"1985","unstructured":"Arslanov, M.M.: Structural properties of the degrees below $${\\bf 0} ^{\\prime }$$. Sov. Math. Dokl. N.S. 283, 270\u2013273 (1985)","journal-title":"Sov. Math. Dokl. N.S."},{"key":"27_CR2","first-page":"27","volume":"7","author":"MM Arslanov","year":"1988","unstructured":"Arslanov, M.M.: On the upper semilattice of Turing degrees below $${\\bf 0}^{\\prime }$$. Russ. Math. (Iz. VUZ) 7, 27\u201333 (1988)","journal-title":"Russ. Math. (Iz. VUZ)"},{"key":"27_CR3","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1002\/1521-3870(200008)46:3<409::AID-MALQ409>3.0.CO;2-P","volume":"46","author":"MM Arslanov","year":"2000","unstructured":"Arslanov, M.M., Cooper, S.B., Li, A.: There is no low maximal d.c.e. degree. Math. Logic Quart. 46, 409\u2013416 (2000)","journal-title":"Math. Logic Quart."},{"key":"27_CR4","doi-asserted-by":"publisher","first-page":"628","DOI":"10.1002\/malq.200410006","volume":"50","author":"MM Arslanov","year":"2004","unstructured":"Arslanov, M.M., Cooper, S.B., Li, A.: There is no low maximal d.c.e. degree - Corrigendum. Math. Logic Quart. 50, 628\u2013636 (2004)","journal-title":"Math. Logic Quart."},{"key":"27_CR5","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s001530100078","volume":"40","author":"MM Arslanov","year":"2001","unstructured":"Arslanov, M.M., Kalimullin, I.S., Sorbi, A.: Density results in the $$\\Delta ^0_2$$ e-degrees. Arch. Math. Logic 40, 597\u2013614 (2001)","journal-title":"Arch. Math. Logic"},{"key":"27_CR6","doi-asserted-by":"publisher","first-page":"401","DOI":"10.2178\/jsl\/1268917488","volume":"75","author":"MM Arslanov","year":"2010","unstructured":"Arslanov, M.M., Kalimullin, I.S., Lempp, S.: On Downey\u2019s conjecture. J. Symb. Logic 75, 401\u2013441 (2010)","journal-title":"J. Symb. Logic"},{"key":"27_CR7","doi-asserted-by":"publisher","first-page":"411","DOI":"10.2307\/2586839","volume":"63","author":"MM Arslanov","year":"1998","unstructured":"Arslanov, M.M., LaForte, G., Slaman, T.A.: Relative enumerability in the difference hierarchy. J. Symb. Logic 63, 411\u2013420 (1998)","journal-title":"J. Symb. Logic"},{"key":"27_CR8","unstructured":"Cooper, S.B.: Degrees of Unsolvability. Ph.D. Thesis, Leicester University, Leicester, England (1971)"},{"key":"27_CR9","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/BF01370692","volume":"31","author":"SB Cooper","year":"1991","unstructured":"Cooper, S.B.: The density of the low$$_2$$ n-r.e. degrees. Arch. Math. Logic 31, 19\u201324 (1991)","journal-title":"Arch. Math. Logic"},{"key":"27_CR10","first-page":"461","volume":"115","author":"SB Cooper","year":"1992","unstructured":"Cooper, S.B.: A splitting theorem for the n-r.e. degrees. Proc. Am. Math. Soc. 115, 461\u2013471 (1992)","journal-title":"Proc. Am. Math. Soc."},{"key":"27_CR11","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/0168-0072(91)90005-7","volume":"55","author":"SB Cooper","year":"1991","unstructured":"Cooper, S.B., Harrington, L., Lachlan, A.H., Lempp, S., Soare, R.I.: The $$d$$-r.e. degrees are not dense. Ann. Pure Appl. Logic 55, 125\u2013151 (1991)","journal-title":"Ann. Pure Appl. Logic"},{"key":"27_CR12","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s101140100150","volume":"18","author":"SB Cooper","year":"2000","unstructured":"Cooper, S.B., Li, A.: Non-uniformity and generalised Sacks splitting. Acta Math. Sin., Engl. Ser. 18, 327\u2013334 (2000a)","journal-title":"Acta Math. Sin., Engl. Ser."},{"key":"27_CR13","doi-asserted-by":"crossref","unstructured":"Cooper, S.B., Li, A.: Splitting and cone avoidance in the d.c.e. degrees. Sci. China (Ser. A) 45, 1135\u20131146 (2002b)","DOI":"10.1360\/02ys9124"},{"key":"27_CR14","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1112\/blms\/21.1.43","volume":"21","author":"RG Downey","year":"1989","unstructured":"Downey, R.G.: D.r.e. degrees and the nondiamond theorem. Bull. London Math. Soc. 21, 43\u201350 (1989)","journal-title":"Bull. London Math. Soc."},{"key":"27_CR15","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/S0168-0072(97)00066-3","volume":"94","author":"RG Downey","year":"1997","unstructured":"Downey, R.G., Shore, R.A.: Splitting theorems and the jump operator. Ann. Pure Appl. Logic 94, 45\u201352 (1997)","journal-title":"Ann. Pure Appl. Logic"},{"key":"27_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0168-0072(93)90234-5","volume":"65","author":"RG Downey","year":"1993","unstructured":"Downey, R.G., Stob, M.: Splitting theorems in recursion theory. Ann. Pure Appl. Logic 65, 1\u2013106 (1993)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"3","key":"27_CR17","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1305\/ndjfl\/1099080209","volume":"45","author":"RG Downey","year":"2004","unstructured":"Downey, R.G., Yu, L.: There are no maximal low d.c.e. degrees. Notre Dame J. Formal Logic 45(3), 147\u2013159 (2004)","journal-title":"Notre Dame J. Formal Logic"},{"issue":"1","key":"27_CR18","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/BF02218750","volume":"7","author":"YL Ershov","year":"1968","unstructured":"Ershov, Y.L.: On a hierarchy of sets I. Algebra Logika 7(1), 47\u201373 (1968a)","journal-title":"Algebra Logika"},{"issue":"4","key":"27_CR19","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF02218664","volume":"7","author":"YL Ershov","year":"1968","unstructured":"Ershov, Y.L.: On a hierarchy of sets II. Algebra Logika 7(4), 15\u201347 (1968b)","journal-title":"Algebra Logika"},{"issue":"1","key":"27_CR20","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/BF02219847","volume":"9","author":"YL Ershov","year":"1970","unstructured":"Ershov, Y.L.: On a hierarchy of sets III. Algebra Logika 9(1), 34\u201351 (1970)","journal-title":"Algebra Logika"},{"key":"27_CR21","doi-asserted-by":"publisher","first-page":"51","DOI":"10.3103\/S1066369X10120066","volume":"12","author":"MK Faizrakhmanov","year":"2010","unstructured":"Faizrakhmanov, M.K.: Decomposability of low 2-computably enumerable degrees and Turing jumps in the Ershov hierarchy. Russ. Math. (Iz. VUZ) 12, 51\u201358 (2010)","journal-title":"Russ. Math. (Iz. VUZ)"},{"key":"27_CR22","doi-asserted-by":"publisher","first-page":"733","DOI":"10.1007\/s00153-013-0340-0","volume":"52","author":"C Fang","year":"2013","unstructured":"Fang, C., Wu, G., Yamaleev, M.M.: On a problem of Ishmukhametov. Arch. Math. Logic 52, 733\u2013741 (2013)","journal-title":"Arch. Math. Logic"},{"key":"27_CR23","doi-asserted-by":"publisher","first-page":"4873","DOI":"10.1090\/S0002-9947-2014-06157-6","volume":"367","author":"HA Ganchev","year":"2015","unstructured":"Ganchev, H.A., Soskova, M.I.: Definability via Kalimullin pairs in the structure of the enumeration degrees. Trans. Am. Math. Soc. 367, 4873\u20134893 (2015)","journal-title":"Trans. Am. Math. Soc."},{"key":"27_CR24","doi-asserted-by":"publisher","first-page":"28","DOI":"10.2307\/2270580","volume":"30","author":"EM Gold","year":"1965","unstructured":"Gold, E.M.: Limiting recursion. J. Symb. Logic 30, 28\u201348 (1965)","journal-title":"J. Symb. Logic"},{"key":"27_CR25","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1007\/s001530050132","volume":"38","author":"SN Ishmukhametov","year":"1999","unstructured":"Ishmukhametov, S.N.: On the r.e. predecessors of d.r.e. degrees. Arch. Math. Logic 38, 373\u2013386 (1999)","journal-title":"Arch. Math. Logic"},{"key":"27_CR26","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s001530050139","volume":"39","author":"ST Ishmukhametov","year":"2000","unstructured":"Ishmukhametov, S.T.: On relative enumerability of Turing degrees. Arch. Math. Logik Grundl. 39, 145\u2013154 (2000)","journal-title":"Arch. Math. Logik Grundl."},{"issue":"4","key":"27_CR27","first-page":"22","volume":"45","author":"IS Kalimullin","year":"2001","unstructured":"Kalimullin, I.S.: Elementary theories of semilattices of n-recursive enumerable degrees with respect to enumerability. Russ. Math. (Iz. VUZ) 45(4), 22\u201325 (2001)","journal-title":"Russ. Math. (Iz. VUZ)"},{"key":"27_CR28","doi-asserted-by":"publisher","first-page":"537","DOI":"10.2178\/jsl\/1190150096","volume":"67","author":"IS Kalimullin","year":"2002","unstructured":"Kalimullin, I.S.: Splitting properties of n-c.e. enumeration degrees. J. Symbolic Logic 67, 537\u2013546 (2002)","journal-title":"J. Symbolic Logic"},{"issue":"2","key":"27_CR29","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1142\/S0219061303000285","volume":"3","author":"IS Kalimullin","year":"2003","unstructured":"Kalimullin, I.S.: Definability of the jump operator in the enumeration degrees. J. Math. Logic 3(2), 257\u2013267 (2003)","journal-title":"J. Math. Logic"},{"key":"27_CR30","doi-asserted-by":"publisher","first-page":"277","DOI":"10.2178\/jsl\/1174668395","volume":"72","author":"IS Kalimullin","year":"2007","unstructured":"Kalimullin, I.S.: Elementary differences between the (2p)-c.e. and the (2p+1)-c.e. enumeration degrees. J. Symbolic Logic 72, 277\u2013284 (2007)","journal-title":"J. Symbolic Logic"},{"key":"27_CR31","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1112\/plms\/s3-16.1.537","volume":"16","author":"AH Lachlan","year":"1966","unstructured":"Lachlan, A.H.: Lower bounds for pairs of recursively enumerable degrees. Proc. London Math. Soc. 16, 537\u2013569 (1966)","journal-title":"Proc. London Math. Soc."},{"key":"27_CR32","doi-asserted-by":"publisher","first-page":"49","DOI":"10.2307\/2270581","volume":"30","author":"H Putnam","year":"1965","unstructured":"Putnam, H.: Trial and error predicates and the solution to a problem of Mostowski. J. Symb. Logic 30, 49\u201357 (1965)","journal-title":"J. Symb. Logic"},{"key":"27_CR33","volume-title":"Theory of Recursive Functions and Effective Computability","author":"H Rogers Jr","year":"1967","unstructured":"Rogers Jr., H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)"},{"key":"27_CR34","unstructured":"Welch, L.: A hierarchy of families of recursively enumerable degrees and a theorem of founding minimal pairs. Ph.D. Thesis (University of Illinois, Urbana, 1980) (1980)"},{"issue":"2","key":"27_CR35","first-page":"204","volume":"154","author":"G Wu","year":"2012","unstructured":"Wu, G., Yamaleev, M.M.: Isolation: motivations and applications. Uchenue Zapiski Kazanskogo Universiteta 154(2), 204\u2013217 (2012)","journal-title":"Uchenue Zapiski Kazanskogo Universiteta"},{"key":"27_CR36","first-page":"76","volume":"6","author":"MM Yamaleev","year":"2009","unstructured":"Yamaleev, M.M.: The splitting of 2-computably enumerable degrees avoiding the upper cones. Russ. Math. (Iz. VUZ) 6, 76\u201380 (2009)","journal-title":"Russ. Math. (Iz. VUZ)"}],"container-title":["Lecture Notes in Computer Science","Computability and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-50062-1_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T16:57:56Z","timestamp":1709830676000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-50062-1_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,1]]},"ISBN":["9783319500614","9783319500621"],"references-count":36,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-50062-1_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016,12,1]]},"assertion":[{"value":"1 December 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}