{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T05:40:18Z","timestamp":1698385218915},"reference-count":3,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4334,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Concerning Post's problem for Kleene degrees and its relativization, Hrbacek showed in [1] and [2] that if <jats:italic>V<\/jats:italic> = <jats:italic>L<\/jats:italic>, then Kleene degrees of coanalytic sets are dense, and then for all <jats:italic>K<\/jats:italic> \u2286<jats:sup>\u03c9<\/jats:sup>\u03c9, there are N<jats:sub>1<\/jats:sub> sets which are Kleene semirecursive in <jats:italic>K<\/jats:italic> and not Kleene recursive in each other and <jats:italic>K.<\/jats:italic> But the density of Kleene semirecursive in <jats:italic>K<\/jats:italic> Kleene degrees is not obtained from these theorems. In this note, we extend these theorems by showing that if <jats:italic>V = L<\/jats:italic>, then for all <jats:italic>K \u2286 <jats:sup>\u03c9<\/jats:sup>\u03c9<\/jats:italic>, Kleene semirecursive in <jats:italic>K<\/jats:italic> Kleene degrees are dense above <jats:italic>K<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/malq.19950410205","type":"journal-article","created":{"date-parts":[[2007,6,2]],"date-time":"2007-06-02T21:17:12Z","timestamp":1180819032000},"page":"183-189","source":"Crossref","is-referenced-by-count":1,"title":["Local Density of Kleene Degrees"],"prefix":"10.1002","volume":"41","author":[{"given":"Hisato","family":"Muraki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19780242506"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19830290204"},{"key":"e_1_2_1_4_2","unstructured":"Weitkamp G. Kleene recursion over the continuum. Ph.D. Thesis Pennsylvania State University1980."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19950410205","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19950410205","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T19:51:38Z","timestamp":1698349898000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19950410205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":3,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/malq.19950410205"],"URL":"https:\/\/doi.org\/10.1002\/malq.19950410205","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}