{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,12]],"date-time":"2022-06-12T21:15:24Z","timestamp":1655068524723},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1288,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We say a countable model <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002498_inline1\" \/> has a <jats:italic>0-basis<\/jats:italic> if the types realized in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002498_inline1\" \/> are uniformly computable. We say <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002498_inline1\" \/> has a (<jats:italic><jats:bold>d<\/jats:bold><\/jats:italic>-)decidable copy if there exists a model <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002498_inline2\" \/> \u2245 <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002498_inline1\" \/>such that the elementary diagram of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002498_inline2\" \/> is (<jats:italic><jats:bold>d<\/jats:bold><\/jats:italic>-)computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous model <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002498_inline1\" \/> with a <jats:italic>0<\/jats:italic>-basis but no decidable copy. We extend this result here. Let <jats:italic><jats:bold>d<\/jats:bold><\/jats:italic> \u2264 0\u2032 be any low<jats:sub>2<\/jats:sub> degree. We show that there exists a homogeneous model <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002498_inline1\" \/> with a <jats:italic>0<\/jats:italic>-basis but no <jats:italic><jats:bold>d<\/jats:bold><\/jats:italic>-decidable copy. A degree <jats:italic><jats:bold>d<\/jats:bold><\/jats:italic> is <jats:italic>0-basis homogeneous bounding<\/jats:italic> if any homogenous <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002498_inline1\" \/> with a <jats:italic>0<\/jats:italic>-basis has a <jats:italic><jats:bold>d<\/jats:bold><\/jats:italic>-decidable copy. In previous work, we showed that the non low<jats:sub>2<\/jats:sub> \u0394<jats:sub arrange=\"stack\">2<\/jats:sub><jats:sup arrange=\"stack\">0<\/jats:sup> degrees are <jats:italic>0<\/jats:italic>-basis homogeneous bounding. The result of this paper shows that this is an exact characterization of the <jats:italic>0<\/jats:italic>-basis homogeneous bounding \u0394<jats:sub arrange=\"stack\">2<\/jats:sub><jats:sup arrange=\"stack\">0<\/jats:sup> degrees.<\/jats:p>","DOI":"10.2178\/jsl\/1278682211","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T13:30:45Z","timestamp":1278682245000},"page":"971-995","source":"Crossref","is-referenced-by-count":1,"title":["A characterization of the <i>0<\/i>-basis homogeneous bounding degrees"],"prefix":"10.1017","volume":"75","author":[{"given":"Karen","family":"Lange","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002498_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-09-04847-8"},{"key":"S0022481200002498_ref012","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1972-113-9"},{"key":"S0022481200002498_ref017","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90030-X"},{"key":"S0022481200002498_ref002","volume-title":"Model theory","volume":"73","author":"Chang","year":"1990"},{"key":"S0022481200002498_ref021","volume-title":"Computability theory and applications","author":"Soare"},{"key":"S0022481200002498_ref006","first-page":"1373","volume":"73","author":"Epstein","year":"2008","journal-title":"Prime models of computably enumerable degree"},{"key":"S0022481200002498_ref015","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1172787551"},{"key":"S0022481200002498_ref005","first-page":"1117","volume":"69","author":"Csima","year":"2004","journal-title":"Bounding prime models"},{"key":"S0022481200002498_ref014","first-page":"1009","volume":"73","author":"Lange","year":"2008","journal-title":"The degree spectra of homogeneous models"},{"key":"S0022481200002498_ref013","first-page":"1034","volume":"51","author":"Knight","year":"1986","journal-title":"Degrees coded in jumps of orderings"},{"key":"S0022481200002498_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01674776"},{"key":"S0022481200002498_ref001","volume-title":"Computable structures and the hyperarithmetical hierarchy","volume":"144","author":"Ash","year":"2000"},{"key":"S0022481200002498_ref003","first-page":"430","volume":"69","author":"Csima","year":"2004","journal-title":"Degree spectra of prime models"},{"key":"S0022481200002498_ref004","first-page":"305","volume":"72","author":"Csima","year":"2007","journal-title":"Bounding homogeneous models"},{"key":"S0022481200002498_ref008","first-page":"3","volume-title":"Handbook of recursive mathematics","volume":"138","author":"Harizanov","year":"1998"},{"key":"S0022481200002498_ref009","unstructured":"Hirschfeldt D.R. , Lange K.M. , and Shore R.A. , The homogeneous model theorem, in preparation."},{"key":"S0022481200002498_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-05-08097-4"},{"key":"S0022481200002498_ref016","volume-title":"Model theory: An introduction","volume":"217","author":"Marker","year":"2002"},{"key":"S0022481200002498_ref018","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1980.91.407"},{"key":"S0022481200002498_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/BF01674780"},{"key":"S0022481200002498_ref020","volume-title":"Recursively enumerable sets and degrees; A study of computable functions and computably generated sets","author":"Soare","year":"1987"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002498","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T21:38:48Z","timestamp":1556401128000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002498\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S0022481200002498"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1278682211","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9]]}}}