{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T09:44:31Z","timestamp":1698486271322},"reference-count":12,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3603,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1997,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider the strongest (most restricted) forms of enumeration reducibility, those that occur between 1\u2010 and npm\u2010reducibility inclusive. By defining two new reducibilities (which we call n1\u2010 and ni\u2010reducibility) which are counterparts to 1\u2010 and i\u2010reducibility, respectively, in the same way that nm\u2010 and npm\u2010reducibility are counterparts to m\u2010 and pm\u2010reducibility, respectively, we bring out the structure (under the natural relation on reducibilities strong with respect to') of the strong reducibilities. By further restricting n1\u2010 and nm\u2010reducibility we are able to define infinite families of reducibilities which isomorphically embed the r. e. Turing degrees. Thus the many well\u2010known results in the theory of the r. e. Turing degrees have counterparts in the theory of strong reducibilities. We are also able to positively answer the question of whether there exist distinct reducibilities \u2264<jats:sub>y<\/jats:sub> and \u2264<jats:sub>a<\/jats:sub> between \u2264<jats:sub>e<\/jats:sub> and \u2264<jats:sub>m<\/jats:sub> such that there exists a non\u2010trivial \u2264<jats:sub>y<\/jats:sub>\u2010contiguous \u2264<jats:sub>z<\/jats:sub> degree.<\/jats:p>","DOI":"10.1002\/malq.19970430411","type":"journal-article","created":{"date-parts":[[2007,5,31]],"date-time":"2007-05-31T05:00:18Z","timestamp":1180587618000},"page":"559-568","source":"Crossref","is-referenced-by-count":0,"title":["Embeddings in the Strong Reducibilities Between 1 and npm"],"prefix":"10.1002","volume":"43","author":[{"given":"Phil","family":"Watson","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"Cooper S. B. Enumeration reducibility non\u2010deterministic computations and relative computability of partial functions. Preprint No. 32\/90 University of Leeds1990.","DOI":"10.1007\/BFb0086114"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19590050703"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1090\/S0002-9947-1969-0245439-X","article-title":"Relationships between reducibilities","volume":"142","author":"Jockusch C. G.","year":"1969","journal-title":"Trans. Amer. Math. Soc."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1969.29.351"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1970-010-6"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1981-14863-1"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1944-08111-1"},{"key":"e_1_2_1_9_2","volume-title":"Theory of Recursive Functions and Effective Computability","author":"Rogers H.","year":"1967"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/1970393"},{"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":"10.1016\/0168-0072(90)90051-3"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19970430411","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19970430411","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T02:07:49Z","timestamp":1698458869000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19970430411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1997,1]]}},"alternative-id":["10.1002\/malq.19970430411"],"URL":"https:\/\/doi.org\/10.1002\/malq.19970430411","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}