{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T16:50:03Z","timestamp":1791564603581,"version":"4.3.4"},"reference-count":11,"publisher":"Duke University Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Notre Dame J. Formal Logic"],"published-print":{"date-parts":[[2016,1,1]]},"abstract":"<jats:p>For a computable structure M, the categoricity spectrum is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable copies of M. If the spectrum has a least degree, this degree is called the degree of categoricity of M. In this paper we investigate spectra of categoricity for computable rigid structures. In particular, we give examples of rigid structures without degrees of categoricity.<\/jats:p>","DOI":"10.1215\/00294527-3322017","type":"journal-article","created":{"date-parts":[[2015,10,30]],"date-time":"2015-10-30T09:11:20Z","timestamp":1446196280000},"page":"45-57","source":"Crossref","is-referenced-by-count":22,"title":["Categoricity Spectra for Rigid Structures"],"prefix":"10.1215","volume":"57","author":[{"given":"Ekaterina","family":"Fokina","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrey","family":"Frolov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Iskander","family":"Kalimullin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"73","reference":[{"key":"1","unstructured":"[1] Anderson, B. A., and B. F. Csima, \u201cDegrees that are not degrees of categoricity,\u201d to appera in Notre Dame Journal of Formal Logic, preprint, <a href=\"arXiv:1210.4220v2\">arXiv:1210.4220v2<\/a> [math.LO]."},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] Hirschfeldt, D. R., B. Khoussainov, R. A. Shore, and A. M. Slinko, \u201cDegree spectra and computable dimensions in algebraic structures,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 115 (2002), pp. 71\u2013113.","DOI":"10.1016\/S0168-0072(01)00087-2"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] Csima, B. F., J. N. Y. Franklin, and R. A. Shore, \u201cDegrees of categoricity and the hyperarithmetic hierarchy,\u201d <i>Notre Dame Journal of Formal Logic<\/i>, vol. 54 (2013), pp. 215\u201331.","DOI":"10.1215\/00294527-1960479"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] Fokina, E. B., I. Kalimullin, and R. Miller, \u201cDegrees of categoricity of computable structures,\u201d <i>Archive for Mathematical Logic<\/i>, vol. 49 (2010), pp. 51\u201367.","DOI":"10.1007\/s00153-009-0160-4"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] Fr\u00f6hlich, A., and J. C. Shepherdson, \u201cEffective procedures in field theory,\u201d <i>Philosophical Transactions of the Royal Society of London Series A<\/i>, vol. 248 (1956), pp. 407\u201332.","DOI":"10.1098\/rsta.1956.0003"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] Goncharov, S. S., \u201cAutostable models and algorithmic dimensions,\u201d pp. 261\u201387 in <i>Handbook of Recursive Mathematics, Vol. 1<\/i>, vol. 138 of <i>Studies in Logic and the Foundations of Mathematics<\/i>, North-Holland, Amsterdam, 1998.","DOI":"10.1016\/S0049-237X(98)80007-4"},{"key":"7","unstructured":"[7] Mal\u2019cev, A. I., \u201cConstructive algebras, I,\u201d <i>Uspekhi Mathematicheskikh Nauk<\/i>, vol. 16 (1961), pp. 3\u201360."},{"key":"8","unstructured":"[8] Mal\u2019cev, A. I., \u201cOn recursive Abelian groups,\u201d <i>Doklady Akademiya Nauk SSSR<\/i>, vol. 146 (1962), pp. 1009\u201312."},{"key":"9","doi-asserted-by":"publisher","unstructured":"[9] Miller, R., \u201c$d$-computable categoricity for algebraic fields,\u201d <i>Journal of Symbolic Logic<\/i>, vol. 74 (2009), pp. 1325\u201351.","DOI":"10.2178\/jsl\/1254748694"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] Richter, L. J., \u201cDegrees of structures,\u201d <i>Journal of Symbolic Logic<\/i>, vol. 46 (1981), pp. 723\u201331.","DOI":"10.2307\/2273222"},{"key":"11","unstructured":"[11] Rodgers, H., <i>Theory of Recursive Functions and Effective Computability<\/i>, Massachusetts Institute of Technology Press, Cambridge, Mass., 1987."}],"container-title":["Notre Dame Journal of Formal Logic"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/journalArticle\/Download?urlid=10.1215\/00294527-3322017","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T15:53:32Z","timestamp":1791561212000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/notre-dame-journal-of-formal-logic\/volume-57\/issue-1\/Categoricity-Spectra-for-Rigid-Structures\/10.1215\/00294527-3322017.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,1]]},"references-count":11,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,1]]}},"URL":"https:\/\/doi.org\/10.1215\/00294527-3322017","relation":{},"ISSN":["0029-4527","1939-0726"],"issn-type":[{"value":"0029-4527","type":"print"},{"value":"1939-0726","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,1]]}}}