{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:53:45Z","timestamp":1777517625904,"version":"3.51.4"},"reference-count":25,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"name":"SRNSFG","award":["FR-22-16379"],"award-info":[{"award-number":["FR-22-16379"]}]},{"name":"ANID Fondecyt Postdoctorado","award":["3230263"],"award-info":[{"award-number":["3230263"]}]},{"DOI":"10.13039\/501100003407","name":"MIUR","doi-asserted-by":"crossref","award":["PRIN 2022 ``Logical Methods in Combinatorics'' No.~2022BXH4R5"],"award-info":[{"award-number":["PRIN 2022 ``Logical Methods in Combinatorics'' No.~2022BXH4R5"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Computability"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:p>\n                    We study immunity properties of the transversals of computably enumerable equivalence relations (or, briefly,\n                    <jats:italic toggle=\"yes\">ceers<\/jats:italic>\n                    ), where a\n                    <jats:italic toggle=\"yes\">transversal<\/jats:italic>\n                    is a set which picks at most one element from every equivalence class of the given equivalence relation. Among transversals, a particular role is played by the\n                    <jats:italic toggle=\"yes\">principal transversal<\/jats:italic>\n                    , whose members are the least elements of the various equivalence classes. While hyperimmunity of the principal transversal implies hyperimmunity of every infinite transversal, we show that this fails both for immunity and hyperhyperimmunity. In both cases, counterexamples are taken from the class of\n                    <jats:italic toggle=\"yes\">interval ceers<\/jats:italic>\n                    , that is, ceers whose equivalence classes are either singletons or intervals of maximal length consisting of consecutive elements of some given c.e. set. We also look into the class of\n                    <jats:italic toggle=\"yes\">hyperdark<\/jats:italic>\n                    ceers, that is, those ceers with infinitely many classes, whose infinite transversals are all hyperimmune, analyzing how this property relates to other computability theoretic properties of the infinite transversals. We make some preliminary observations on the\n                    <jats:italic toggle=\"yes\">hyperhyperdark<\/jats:italic>\n                    ceers, that is, those ceers with infinitely many classes, whose infinite transversals are all hyperhyperimmune.\n                  <\/jats:p>","DOI":"10.1177\/22113568241296546","type":"journal-article","created":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T10:47:59Z","timestamp":1765363679000},"page":"111-127","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["On the transversals of a ceer"],"prefix":"10.1177","volume":"14","author":[{"given":"Irakli","family":"Chitaia","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia"}]},{"given":"Valentino","family":"Delle Rose","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Informatica, Automatica e Gestionale \u201cAntonio Ruberti,\u201d Universit\u00e0 degli Studi di Roma \u201cLa Sapienza,\u201d Roma, Italy"},{"name":"Instituto de Ingenier\u00eda Matem\u00e1tica y Computacional, Pontificia Universidad Cat\u00f3lica de Chile, Macul (Santiago), Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9288-3290","authenticated-orcid":false,"given":"Andrea","family":"Sorbi","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Informatica e Scienze Matematiche, Universit\u00e0 degli Studi di Siena, Siena, Italy"}]}],"member":"179","published-online":{"date-parts":[[2025,12,10]]},"reference":[{"key":"e_1_3_4_2_2","first-page":"3","article-title":"Finitely generated enumerable and absolutely locally finite algebras","volume":"116","author":"Kasymov NKH","year":"1986","unstructured":"Kasymov NKH, Khoussainov BM. Finitely generated enumerable and absolutely locally finite algebras. Vychisl Sistemy 1986; 116: 3\u201315.","journal-title":"Vychisl Sistemy"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2015.11.042"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196723500339"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.3233\/COM-180098"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010521410739"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19940400407"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2013.8"},{"key":"e_1_3_4_9_2","doi-asserted-by":"crossref","unstructured":"Andrews U Badaev S Sorbi A. A survey on universal computably enumerable equivalence relations. In: Day A Fellows M Greenberg N et al. (eds) Computability and complexity. Essays dedicated to Rodney G. Downey on the occasion of his 60th birthday. Cham: Springer 2017 pp.418\u2013451.","DOI":"10.1007\/978-3-319-50062-1_25"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2020.102811"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2022.14"},{"key":"e_1_3_4_12_2","doi-asserted-by":"crossref","unstructured":"Selivanov V. Positive structures. In: Cooper SB and Goncharov SS (eds) Computability and models. New York: Springer 2003 pp.321\u2013350.","DOI":"10.1007\/978-1-4615-0755-0_14"},{"key":"e_1_3_4_13_2","doi-asserted-by":"crossref","unstructured":"Khoussainov B. A journey to computably enumerable structures (tutorial lectures). In: Sailing routes in the world of computation \u2013 Proceedings of the 14th conference on computability in Europe (CiE 2018) Kiel Germany 30 July\u20133 August 2018 (eds F Manea RG\u00a0Miller and D Nowotka) vol. 10936 of LNCS 2018 pp.1\u201319. 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