{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T05:40:20Z","timestamp":1698385220347},"reference-count":8,"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>The main results of the present paper are the following theorems: 1. There is no <jats:italic>e \u2208 \u03c9<\/jats:italic> such that for any <jats:italic>A, B<\/jats:italic> \u2286 \u03c9, <jats:italic>S<\/jats:italic><jats:sup><jats:italic>A<\/jats:italic><\/jats:sup> = <jats:italic>W<\/jats:italic><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-1.gif\" xlink:title=\"urn:x-wiley:09425616:media:MALQ19950410202:tex2gif-stack-1\" \/> is simple in <jats:italic>A<\/jats:italic>, and if <jats:italic>A\u2032<\/jats:italic> \uf8fd<jats:sub>T<\/jats:sub> <jats:italic>B<\/jats:italic>\u2032, then <jats:italic>S<\/jats:italic><jats:sup><jats:italic>A<\/jats:italic><\/jats:sup> =* <jats:italic>S<\/jats:italic><jats:sup><jats:italic>B<\/jats:italic><\/jats:sup>. 2 There is an <jats:italic>e<\/jats:italic> \u2208 \u03c9 such that for any <jats:italic>A, B<\/jats:italic> \u2286 \u03c9, <jats:italic>M<\/jats:italic><jats:sup><jats:italic>A<\/jats:italic><\/jats:sup> = <jats:italic>W<\/jats:italic><jats:sub><jats:italic>e<\/jats:italic><\/jats:sub> is incomplete maximal in <jats:italic>A<\/jats:italic>, and if <jats:italic>A =* B<\/jats:italic>, then <jats:italic>M<\/jats:italic><jats:sup><jats:italic>A<\/jats:italic><\/jats:sup> \uf8fd<jats:sub>T<\/jats:sub> <jats:italic>M<\/jats:italic><jats:sup><jats:italic>B<\/jats:italic><\/jats:sup>.<\/jats:p>","DOI":"10.1002\/malq.19950410202","type":"journal-article","created":{"date-parts":[[2007,6,2]],"date-time":"2007-06-02T21:18:03Z","timestamp":1180819083000},"page":"143-160","source":"Crossref","is-referenced-by-count":0,"title":["Invariant Constructions of Simple and Maximal Sets"],"prefix":"10.1002","volume":"41","author":[{"given":"Frank P.","family":"Weber","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":"10.2307\/2274816"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272164"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21755-9"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2035242"},{"key":"e_1_2_1_6_2","volume-title":"Cabal Seminar 81\u201385, 37\u201355, Lecture Notes in Mathematics 1333","author":"Slaman T.","year":"1988"},{"key":"e_1_2_1_7_2","volume-title":"Recursively Enumerable Sets and Degrees","author":"Soare R. I.","year":"1986"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/2273146"},{"key":"e_1_2_1_9_2","unstructured":"Ye Hong Some Properties of Recursively Enumerable Sets Uniform for Equivalence Relations. Ph. D. thesis University of Connecticut1988."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19950410202","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19950410202","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T19:51:12Z","timestamp":1698349872000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19950410202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/malq.19950410202"],"URL":"https:\/\/doi.org\/10.1002\/malq.19950410202","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]]}}}