{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:39:20Z","timestamp":1774625960516,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":9232,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1988,12]]},"abstract":"<jats:p>A recursively enumerable splitting of an r.e. set <jats:italic>A<\/jats:italic> is a pair of r.e. sets <jats:italic>B<\/jats:italic> and <jats:italic>C<\/jats:italic> such that <jats:italic>A<\/jats:italic> = <jats:italic>B<\/jats:italic> \u222a <jats:italic>C<\/jats:italic> and <jats:italic>B<\/jats:italic> \u2229 <jats:italic>C<\/jats:italic> = \u2298. Since for such a splitting deg <jats:italic>A<\/jats:italic> = deg <jats:italic>B<\/jats:italic> \u222a deg <jats:italic>C<\/jats:italic>, r.e. splittings proved to be a quite useful notion for investigations into the structure of the r.e. degrees. Important splitting theorems, like Sacks splitting [S1], Robinson splitting [R1] and Lachlan splitting [L3], use r.e. splittings.<\/jats:p><jats:p>Since each r.e. splitting of a set induces a splitting of its degree, it is natural to study the relation between the degrees of r.e. splittings and the degree splittings of a set. We say a set <jats:italic>A<\/jats:italic> has the <jats:italic>strong universal splitting property<\/jats:italic> (SUSP) if each splitting of its degree is represented by an r.e. splitting of itself, i.e., if for deg <jats:italic>A<\/jats:italic> = <jats:bold>b<\/jats:bold> \u222a <jats:bold>c<\/jats:bold> there is an r.e. splitting <jats:italic>B, C<\/jats:italic> of <jats:italic>A<\/jats:italic> such that deg <jats:italic>B<\/jats:italic> = <jats:bold>b<\/jats:bold> and deg <jats:italic>C<\/jats:italic> = <jats:bold>c<\/jats:bold>. The goal of this paper is the study of this splitting property.<\/jats:p><jats:p>In the literature some weaker splitting properties have been studied as well as splitting properties which imply failure of the SUSP.<\/jats:p>","DOI":"10.2307\/2274608","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:28:19Z","timestamp":1146954499000},"page":"1110-1137","source":"Crossref","is-referenced-by-count":14,"title":["Degree theoretical splitting properties of recursively enumerable sets"],"prefix":"10.1017","volume":"53","author":[{"given":"Klaus","family":"Ambos-Spies","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter A.","family":"Fejer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200027961","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T10:33:37Z","timestamp":1679481217000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200027961\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,12]]},"references-count":0,"aliases":["10.1017\/s0022481200027961"],"journal-issue":{"issue":"4","published-print":{"date-parts":[[1988,12]]}},"alternative-id":["S0022481200027961"],"URL":"https:\/\/doi.org\/10.2307\/2274608","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,12]]}}}