{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:53:53Z","timestamp":1777517633838,"version":"3.51.4"},"reference-count":29,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2015,7,1]],"date-time":"2015-07-01T00:00:00Z","timestamp":1435708800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Computability"],"published-print":{"date-parts":[[2015,7,24]]},"abstract":"<jats:p>Abstract<\/jats:p>\n                  <jats:p>We prove the existence of a limitwise monotonic function [Formula: see text] such that, for any [Formula: see text] function [Formula: see text], [Formula: see text]. Relativising this result we deduce the existence of an \u03b7-like computable linear ordering [Formula: see text] such that, for any [Formula: see text] function [Formula: see text], and \u03b7-like [Formula: see text] of order type [Formula: see text], [Formula: see text]. We prove directly that, for any computable [Formula: see text] which is either (i) strongly \u03b7-like or (ii) \u03b7-like with no strongly \u03b7-like interval, there exists [Formula: see text]-limitwise monotonic [Formula: see text] such that [Formula: see text] has order type [Formula: see text]. In so doing we provide an alternative proof to the fact that, for every \u03b7-like computable linear ordering [Formula: see text] with no strongly \u03b7-like interval, there exists computable [Formula: see text] with [Formula: see text] block relation. We also use our results to prove the existence of an \u03b7-like computable linear ordering which is [Formula: see text] categorical but not [Formula: see text] categorical.<\/jats:p>","DOI":"10.3233\/com-150037","type":"journal-article","created":{"date-parts":[[2015,7,26]],"date-time":"2015-07-26T09:13:12Z","timestamp":1437901992000},"page":"119-139","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["On limitwise monotonicity and maximal block functions"],"prefix":"10.1177","volume":"4","author":[{"given":"Charles M.","family":"Harris","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK. ."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,7,1]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.10.002"},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1023\/A:1006031314563"},{"key":"ref003","unstructured":"[3]S.B.\u00a0Cooper, Computability Theory, CRC Mathematics Series, Chapman and Hall, London, 2004."},{"key":"ref004","doi-asserted-by":"crossref","unstructured":"[4]R.\u00a0Downey, Computability theory and linear orderings, in:\n                      Handbook of Recursive Mathematics, Vol.\n                      2\n                      : Recursive Algebra, Analysis and Combinatorics, Studies in Logic and the Foundations of Mathematics\n                      , Y.L.\u00a0Ershov, S.S.\u00a0Goncharov, A.\u00a0Nerode and J.B.\u00a0Remmel, eds, North Holland, 1998, pp.\u00a0823\u2013976.","DOI":"10.1016\/S0049-237X(98)80047-5"},{"key":"ref005","doi-asserted-by":"crossref","unstructured":"[5]R.G.\u00a0Downey, A.M.\u00a0Kach and D.\u00a0Turetsky, Limitwise monotonic functions and their applications, in: Proceedings of the 11th Asian Logic Conference, T.\u00a0Arai, Q.\u00a0Feng, B.\u00a0Kim, G.\u00a0Wu and Y.\u00a0Yang, eds, World Sci. 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