{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T03:44:35Z","timestamp":1778903075962,"version":"3.51.4"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2024,3,20]],"date-time":"2024-03-20T00:00:00Z","timestamp":1710892800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,3,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In 1998 R. Downey formulated a problem: to describe a property $P$ of classical order types, which guarantees that if $\\mathcal{L}$ is a low linear order and $P$ holds for the order type of $\\mathcal{L}$ then $\\mathcal{L}$ is isomorphic to a computable linear order. We find a new such property $P$. Also, we give an upper bound on a complexity of an isomorphism between computable and low copies and show that this bound is sharp.<\/jats:p>","DOI":"10.1093\/logcom\/exae008","type":"journal-article","created":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T03:49:12Z","timestamp":1710992952000},"source":"Crossref","is-referenced-by-count":4,"title":["Low scattered linear orders"],"prefix":"10.1093","volume":"35","author":[{"given":"Andrey","family":"Frolov","sequence":"first","affiliation":[{"name":"Innopolis University , Innopolis, Universitetskaya str. 1, 420500, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maxim","family":"Zubkov","sequence":"additional","affiliation":[{"name":"N.I. Lobachevsky Institute of Mathematics and Mechanics , Kazan Federal University, Kazan, Kremlevskaya str. 18, 420008, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,3,20]]},"reference":[{"key":"2025030912412808800_ref1","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s10469-009-9067-8","article-title":"Computability on linear orderings enriched with predicates","volume":"48","author":"Alaev","year":"2009","journal-title":"Algebra and Logic"},{"key":"2025030912412808800_ref2","first-page":"823","article-title":"Computability theory and linear orderings","volume-title":"Handbook of Recursive Mathematics","author":"Downey","year":"1998"},{"key":"2025030912412808800_ref3","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1002\/malq.19890350307","article-title":"On choice sets and strongly non-trivial self-embeddings of recursive linear orders","volume":"35","author":"Downey","year":"1989","journal-title":"Mathematical Logic Quarterly"},{"key":"2025030912412808800_ref4","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1134\/S199508021401003X","article-title":"Scattered linear orderings with no computable presentation","volume":"35","author":"Frolov","year":"2014","journal-title":"Lobachevskii Journal of Mathematics"},{"key":"2025030912412808800_ref5","first-page":"201","article-title":"${\\Delta }_2^0$-copies of linear orderings","volume-title":"Algebra and Logic","author":"Frolov","year":"2006"},{"key":"2025030912412808800_ref6","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1007\/s11202-010-0091-7","article-title":"Linear orders of low degree","volume":"51","author":"Frolov","year":"2010","journal-title":"Siberian Mathematical Journal"},{"key":"2025030912412808800_ref7","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1093\/logcom\/exq040","article-title":"Low linear orderings","volume":"22","author":"Frolov","year":"2012","journal-title":"Journal of Logic and Computation"},{"key":"2025030912412808800_ref8","first-page":"81","article-title":"Computable presentability of countable linear orders","volume":"158","author":"Frolov","year":"2018","journal-title":"Progress in Science and Technology. 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