{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T16:11:41Z","timestamp":1698336701128},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5064,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1993,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper introduces the notion of cW10\u2010creative set, which strengthens that of semicreative set in a similar way as complete creativity strengthens creativity. Two results are proven, both of which imply that not all semicreative sets are cW10\u2010creative. First, it is shown that semicreative Dedekind cuts cannot be cW10\u2010creative; the existence of semicreative Dedekind cuts was shown by Soare. Secondly, it is shown that (i) if <jats:italic>A<\/jats:italic> \u2295 <jats:italic>B<\/jats:italic>, the join of <jats:italic>A<\/jats:italic> and <jats:italic>B<\/jats:italic>, is cW10\u2010creative, then either <jats:italic>A<\/jats:italic> or <jats:italic>B<\/jats:italic> is cW10\u2010creative, and (ii) the same is not true with \u2018cW10\u2010creative\u2019 replaced by \u2018semicreative\u2019. Moreover, sets <jats:italic>A<\/jats:italic>, <jats:italic>B<\/jats:italic> which provide a counterexample for (ii) can be constructed within any given nonrecursive r.e. T\u2010degrees a, b. MSC: 03D30.<\/jats:p>","DOI":"10.1002\/malq.19930390106","type":"journal-article","created":{"date-parts":[[2007,6,3]],"date-time":"2007-06-03T01:47:47Z","timestamp":1180835267000},"page":"33-46","source":"Crossref","is-referenced-by-count":0,"title":["A variant of the Notion of Semicreative set"],"prefix":"10.1002","volume":"39","author":[{"given":"Heinrich","family":"Rolletschek","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","article-title":"A note on some variants of the notion of creative set","volume":"139","author":"Buchberger B.","year":"1979","journal-title":"Institutsbericht"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1090\/S0002-9939-1954-0063995-6","article-title":"A theorem on hypersimple sets","volume":"5","author":"Dekker J. C. E.","year":"1954","journal-title":"Proc. Amer. Math. Soc."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/1992952"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2269692"},{"key":"e_1_2_1_6_2","unstructured":"Neubauer R. Eine Systematik der Kreativit\u00e4tsbegriffe (A systematics of creativity concepts). Diploma thesis Institute for Mathematics Johannes Kepler\u2010Universit\u00e4t Linz 1977."},{"key":"e_1_2_1_7_2","volume-title":"Theory of Recursive Functions and Effective Computability","author":"Rogers H.","year":"1967"},{"key":"e_1_2_1_8_2","unstructured":"Rolletschek H. Beitr\u00e4ge zur Systematik der Kreativit\u00e4tsbegriffe. (Contributions to the systematics of creativity concepts). Dissertation Institute for Mathematics Johannes Kepler\u2010Universit\u00e4t Linz 1980."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/1970214"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2033701"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/1995137"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-65-03247-3"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19930390106","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19930390106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T20:59:36Z","timestamp":1698267576000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19930390106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,1]]}},"alternative-id":["10.1002\/malq.19930390106"],"URL":"https:\/\/doi.org\/10.1002\/malq.19930390106","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,1]]}}}