{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T00:03:29Z","timestamp":1775261009372,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"5-6","license":[{"start":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T00:00:00Z","timestamp":1541030400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P27527"],"award-info":[{"award-number":["P27527"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["16-31-60058 mol_a_dk"],"award-info":[{"award-number":["16-31-60058 mol_a_dk"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2019,8]]},"DOI":"10.1007\/s00153-018-0650-3","type":"journal-article","created":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T02:40:44Z","timestamp":1541040044000},"page":"543-563","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Degrees of bi-embeddable categoricity of equivalence structures"],"prefix":"10.1007","volume":"58","author":[{"given":"Nikolay","family":"Bazhenov","sequence":"first","affiliation":[]},{"given":"Ekaterina","family":"Fokina","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3494-9049","authenticated-orcid":false,"given":"Dino","family":"Rossegger","sequence":"additional","affiliation":[]},{"given":"Luca","family":"San Mauro","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,11,1]]},"reference":[{"issue":"950","key":"650_CR1","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1098\/rsta.1956.0003","volume":"248","author":"A Fr\u00f6hlich","year":"1956","unstructured":"Fr\u00f6hlich, A., Shepherdson, J.C.: Effective procedures in field theory. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 248(950), 407\u2013432 (1956)","journal-title":"Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci."},{"key":"650_CR2","unstructured":"Maltsev, A.I.: On recursive Abelian groups. In: Soviet Mathematics, vol. 3. Doklady (1962)"},{"key":"650_CR3","doi-asserted-by":"crossref","unstructured":"Fokina, E., Harizanov, V., Melnikov, A.G.: Computable model theory. Turing\u2019s legacy: developments from Turing\u2019s ideas in logic 42, 124\u2013191 (2014)","DOI":"10.1017\/CBO9781107338579.006"},{"key":"650_CR4","doi-asserted-by":"publisher","first-page":"360","DOI":"10.2178\/jsl\/1120224717","volume":"70","author":"A Montalb\u00e1n","year":"2005","unstructured":"Montalb\u00e1n, A.: Up to equimorphism, hyperarithmetic is recursive. J. Symb. Log. 70, 360\u2013378 (2005)","journal-title":"J. Symb. Log."},{"key":"650_CR5","doi-asserted-by":"publisher","first-page":"71","DOI":"10.2178\/bsl\/1174668219","volume":"13","author":"A Montalb\u00e1n","year":"2007","unstructured":"Montalb\u00e1n, A.: On the equimorphism types of linear orderings. Bull. Symb. Log. 13, 71\u201399 (2007)","journal-title":"Bull. Symb. Log."},{"issue":"3","key":"650_CR6","doi-asserted-by":"publisher","first-page":"1265","DOI":"10.1090\/S0002-9947-07-04285-7","volume":"360","author":"N Greenberg","year":"2008","unstructured":"Greenberg, N., Montalb\u00e1n, A.: Ranked structures and arithmetic transfinite recursion. Trans. Am. Math. Soc. 360(3), 1265\u20131307 (2008)","journal-title":"Trans. Am. Math. Soc."},{"key":"650_CR7","doi-asserted-by":"crossref","unstructured":"Fokina, E., Rossegger, D., Mauro, L.S.: Bi-embeddability spectra and bases of spectra. arXiv preprint arXiv:1808.05451 (2018)","DOI":"10.1002\/malq.201800056"},{"key":"650_CR8","series-title":"Theory and Applications of Computability","volume-title":"Turing Computability","author":"IS Robert","year":"2016","unstructured":"Robert, I.S.: Turing Computability. Theory and Applications of Computability. Springer, Berlin Heidelberg (2016)"},{"key":"650_CR9","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.apal.2005.10.002","volume":"141","author":"W Calvert","year":"2006","unstructured":"Calvert, W., Cenzer, D., Harizanov, V., Morozov, A.: Effective categoricity of equivalence structures. Ann. Pure Appl. Log. 141, 61\u201378 (2006)","journal-title":"Ann. Pure Appl. Log."},{"issue":"1","key":"650_CR10","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/s00153-009-0160-4","volume":"49","author":"E Fokina","year":"2010","unstructured":"Fokina, E., Kalimullin, I.S., Miller, R.: Degrees of categoricity of computable structures. Arch. Math. Log. 49(1), 51\u201367 (2010)","journal-title":"Arch. Math. Log."},{"issue":"12","key":"650_CR11","first-page":"1325","volume":"74","author":"M Russell","year":"2009","unstructured":"Russell, M.: D-computable categoricity for algebraic fields. J. Symb. Log. 74(12), 1325\u20131351 (2009)","journal-title":"J. Symb. Log."},{"issue":"1","key":"650_CR12","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1215\/00294527-3322017","volume":"57","author":"E Fokina","year":"2016","unstructured":"Fokina, E., Frolov, A., Kalimullin, I.S.: Categoricity spectra for rigid structures. Notre Dame J. Form. Log. 57(1), 45\u201357 (2016)","journal-title":"Notre Dame J. Form. Log."},{"issue":"2","key":"650_CR13","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1215\/00294527-1960479","volume":"54","author":"BF Csima","year":"2013","unstructured":"Csima, B.F., Franklin, J.N.Y., Shore, R.A.: Degrees of categoricity and the hyperarithmetic hierarchy. Notre Dame J. Form. Log. 54(2), 215\u2013231 (2013)","journal-title":"Notre Dame J. Form. Log."},{"key":"650_CR14","doi-asserted-by":"crossref","unstructured":"Csima, B.F., Stephenson, J.: Finite computable dimension and degrees of categoricity. Annals of Pure and Applied Logic (2018)","DOI":"10.1016\/j.apal.2018.08.012"},{"issue":"2","key":"650_CR15","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s10469-016-9385-6","volume":"55","author":"NA Bazhenov","year":"2016","unstructured":"Bazhenov, N.A., Kalimullin, I.S., Yamaleev, M.M.: Degrees of categoricity vs. strong degrees of categoricity. Algebra Log. 55(2), 173\u2013177 (2016)","journal-title":"Algebra Log."},{"issue":"1","key":"650_CR16","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1017\/jsl.2017.70","volume":"83","author":"NA Bazhenov","year":"2018","unstructured":"Bazhenov, N.A., Kalimullin, I.S., Yamaleev, M.M.: Degrees of categoricity and spectral dimension. J. Symb. Log. 83(1), 103\u2013116 (2018)","journal-title":"J. Symb. Log."},{"key":"650_CR17","first-page":"143","volume":"39","author":"AM Kach","year":"2009","unstructured":"Kach, A.M., Turetsky, D.: $${\\Delta ^{0}}_2$$ \u0394 0 2 -categoricity of equivalence structures. N. Z. J. Math. 39, 143\u2013149 (2009)","journal-title":"N. Z. J. Math."},{"issue":"9","key":"650_CR18","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1016\/j.apal.2015.04.003","volume":"166","author":"RG Downey","year":"2015","unstructured":"Downey, R.G., Melnikov, A.G., Meng Ng, K.: On $${\\Delta ^{0}}_2$$ \u0394 0 2 -categoricity of equivalence relations. Ann. Pure Appl. Log. 166(9), 851\u2013880 (2015)","journal-title":"Ann. Pure Appl. Log."},{"key":"650_CR19","doi-asserted-by":"crossref","unstructured":"Rodney, G.D., Asher, M.K., Turetsky, D.: Limitwise monotonic functions and their applications. In: Proceedings Of The 11Th Asian Logic Conference, pp. 59\u201385 (2011)","DOI":"10.1142\/9789814360548_0004"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-018-0650-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-018-0650-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-018-0650-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T22:48:34Z","timestamp":1775256514000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-018-0650-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,1]]},"references-count":19,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["650"],"URL":"https:\/\/doi.org\/10.1007\/s00153-018-0650-3","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,1]]},"assertion":[{"value":"6 March 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 October 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}