{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T02:55:39Z","timestamp":1768013739106,"version":"3.49.0"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:p> In this paper, we solve a long-standing open question (see, e.g. Downey [6, Sec. 7] and Downey and Moses [11]), about the spectrum of the successivity relation on a computable linear ordering. We show that if a computable linear ordering [Formula: see text] has infinitely many successivities, then the spectrum of the successivity relation is closed upwards in the computably enumerable Turing degrees. To do this, we use a new method of constructing [Formula: see text]-isomorphisms, which has already found other applications such as Downey, Kastermans and Lempp [9] and is of independent interest. It would seem to promise many further applications. <\/jats:p>","DOI":"10.1142\/s0219061310000924","type":"journal-article","created":{"date-parts":[[2011,5,10]],"date-time":"2011-05-10T10:04:14Z","timestamp":1305021854000},"page":"83-99","source":"Crossref","is-referenced-by-count":10,"title":["ON THE COMPLEXITY OF THE SUCCESSIVITY RELATION IN COMPUTABLE LINEAR ORDERINGS"],"prefix":"10.1142","volume":"10","author":[{"given":"ROD","family":"DOWNEY","sequence":"first","affiliation":[{"name":"School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, Wellington, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"STEFFEN","family":"LEMPP","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Wisconsin Madison, Wisconsin 53706-1388, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GUOHUA","family":"WU","sequence":"additional","affiliation":[{"name":"School of Physical and Mathematical Sciences, Nanyang Technological University Singapore 637371, Republic of Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2307\/2274709"},{"key":"rf2","volume-title":"Computable Structures and Hyperarithmetical Hierarchy","author":"Ash C. 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