{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T20:11:03Z","timestamp":1757621463460,"version":"3.44.0"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T00:00:00Z","timestamp":1753747200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan","award":["AP19676989"],"award-info":[{"award-number":["AP19676989"]}]},{"DOI":"10.13039\/501100020822","name":"Sobolev Institute of Mathematics","doi-asserted-by":"publisher","award":["FWNF-2022-0011"],"award-info":[{"award-number":["FWNF-2022-0011"]}],"id":[{"id":"10.13039\/501100020822","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We prove that there exists a $\\varSigma ^{0}_{1}$ closed subset of $[0,1]$ which is not homeomorphic to any computably compact space. We show that the index set of c.e. subspaces of $[0,1]$ that admit a computably compact presentation is not arithmetical, as witnessed by subsets of $[0,1]$. The index set result is new for computable Polish spaces in general, not only for those realised as c.e. closed subsets of $[0,1]$.<\/jats:p>","DOI":"10.1093\/logcom\/exaf043","type":"journal-article","created":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T00:59:16Z","timestamp":1755046756000},"source":"Crossref","is-referenced-by-count":0,"title":["A non-computable c.e. closed subset of [0,1]"],"prefix":"10.1093","volume":"35","author":[{"given":"Serikzhan","family":"Badaev","sequence":"first","affiliation":[{"name":"Kazakh-British Technical University, School of Applied Mathematics , 59 Tole Bi Street, Almaty, 050000 ,","place":["Kazakhstan"]}]},{"given":"Nikolay","family":"Bazhenov","sequence":"additional","affiliation":[{"name":"Kazakh-British Technical University , School of Applied Mathematics, 59 Tole Bi Street, Almaty, 050000 ,","place":["Kazakhstan"]},{"name":"Sobolev Institute of Mathematics , Laboratory of Computability Theory and Applied Logic, 4 Academician Koptyug Avenue, Novosibirsk, 630090 ,","place":["Russia"]},{"name":"Nazarbayev University , Department of Mathematics, 53 Qabanbaybatyr Avenue, Astana, 010000 ,","place":["Kazakhstan"]}]},{"given":"Sergey","family":"Goncharov","sequence":"additional","affiliation":[{"name":"Sobolev Institute of Mathematics, Laboratory of Computability Theory and Applied Logic , 4 Academician Koptyug Avenue, Novosibirsk, 630090 ,","place":["Russia"]}]},{"given":"Birzhan","family":"Kalmurzayev","sequence":"additional","affiliation":[{"name":"Kazakh-British Technical University , School of Applied Mathematics, 59 Tole Bi Street, Almaty, 050000 ,","place":["Kazakhstan"]}]},{"given":"Alexander","family":"Melnikov","sequence":"additional","affiliation":[{"name":"Victoria University of Wellington , School of Mathematics and Statistics, Kelburn Parade, Wellington, 6012 ,","place":["New Zealand"]}]}],"member":"286","published-online":{"date-parts":[[2025,8,12]]},"reference":[{"key":"2025090809265998300_ref1","doi-asserted-by":"crossref","first-page":"227","DOI":"10.3233\/COM-220430","article-title":"Strong computable type","volume":"12","author":"Amir","year":"2023","journal-title":"Computability"},{"key":"2025090809265998300_ref2","doi-asserted-by":"crossref","first-page":"Paper 103491","DOI":"10.1016\/j.apal.2024.103491","article-title":"Computably and punctually universal spaces","volume":"176","author":"Bagaviev","year":"2025","journal-title":"Annals of Pure and Applied Logic"},{"key":"2025090809265998300_ref3","doi-asserted-by":"crossref","first-page":"103304","DOI":"10.1016\/j.apal.2023.103304","article-title":"Computable Stone spaces","volume":"174","author":"Bazhenov","year":"2023","journal-title":"Annals of Pure and Applied Logic"},{"key":"2025090809265998300_ref4","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.ic.2015.09.001","article-title":"Effective subsets under homeomorphisms of $R^n$","volume":"245","author":"Bosserhoff","year":"2015","journal-title":"Information and Computation"},{"key":"2025090809265998300_ref5","first-page":"paper 8","article-title":"Computability of 1-manifolds","volume":"10","author":"Burnik","year":"2014","journal-title":"Logical Methods in Computer Science"},{"article-title":"Computable Gelfand duality","year":"2024","author":"Burton","key":"2025090809265998300_ref6"},{"key":"2025090809265998300_ref7","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1017\/bsl.2023.16","article-title":"Computably compact metric spaces","volume":"29","author":"Downey","year":"2023","journal-title":"The Bulletin of Symbolic Logic"},{"volume-title":"Countable Structure Theory: A Unified Approach","author":"Downey","key":"2025090809265998300_ref8"},{"volume-title":"General Topology, Volume 6 of Sigma Series in Pure Mathematics","author":"Engelking","key":"2025090809265998300_ref9"},{"key":"2025090809265998300_ref10","doi-asserted-by":"crossref","first-page":"365","DOI":"10.2307\/2270692","article-title":"Hierarchies of Boolean algebras","volume":"35","author":"Feiner","year":"1970","journal-title":"The Journal of Symbolic Logic"},{"volume-title":"Countable Boolean Algebras and Decidability","year":"1997","author":"Goncharov","key":"2025090809265998300_ref11"},{"key":"2025090809265998300_ref12","doi-asserted-by":"crossref","first-page":"1664","DOI":"10.1017\/jsl.2020.67","article-title":"Computability of Polish spaces up to homeomorphism","volume":"85","author":"Harrison-Trainor","year":"2020","journal-title":"The Journal of Symbolic Logic"},{"key":"2025090809265998300_ref13","first-page":"455","article-title":"Subgroups of finitely presented groups","volume":"262","author":"Higman","year":"1961","journal-title":"Proceedings of the Royal Society of London. 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