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Formal Logic"],"published-print":{"date-parts":[[2017,1,1]]},"abstract":"<jats:p>We show that for every computable ordinal of the form \u03b2=\u03b4+2n+1&gt;1, where \u03b4 is zero or a limit ordinal and n\u2208\u03c9, there exists a torsion-free abelian group having an X-computable copy if and only if X is nonlow\u03b2.<\/jats:p>","DOI":"10.1215\/00294527-2017-0006","type":"journal-article","created":{"date-parts":[[2017,5,12]],"date-time":"2017-05-12T22:01:26Z","timestamp":1494626486000},"page":"507-525","source":"Crossref","is-referenced-by-count":6,"title":["New Degree Spectra of Abelian Groups"],"prefix":"10.1215","volume":"58","author":[{"given":"Alexander G.","family":"Melnikov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"73","reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] Andersen, B. M., A. M. Kach, A. G. Melnikov, and R. 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S., <i>Countable Boolean Algebras and Decidability<\/i>, Siberian School of Algebra and Logic, Consultants Bureau, New York, 1997."},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] Hermann, G., \u201cDie Frage der endlich vielen Schritte in der Theorie der Polynomideale\u201d (in German), <i>Mathematische Annalen<\/i>, vol. 95 (1926), pp. 736\u201388.","DOI":"10.1007\/BF01206635"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] Higman, G., \u201cSubgroups of finitely presented groups,\u201d <i>Proceedings of the Royal Society of London, Series A<\/i>, vol. 262 (1961), pp. 455\u201375.","DOI":"10.1098\/rspa.1961.0132"},{"key":"16","doi-asserted-by":"publisher","unstructured":"[16] Jockusch, C. G., and R. I. 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G., \u201cConstructive abelian groups,\u201d pp. 1177\u2013231 in <i>Handbook of Recursive Mathematics, Vol. 2: Recursive Algebra, Analysis and Combinatorics<\/i>, vol. 139 of <i>Studies in Logic and the Foundations of Mathematics<\/i>, North-Holland, Amsterdam, 1998.","DOI":"10.1016\/S0049-237X(98)80050-5"},{"key":"20","doi-asserted-by":"publisher","unstructured":"[20] Knight, J. F., \u201cDegrees coded in jumps of orderings,\u201d <i>Journal of Symbolic Logic<\/i>, vol. 51 (1986), pp. 1034\u201342.","DOI":"10.2307\/2273915"},{"key":"21","unstructured":"[21] Mal\u2019cev, A., \u201cOn recursive abelian groups\u201d (in Russian), <i>Doklady Akademii Nauk SSSR<\/i>, vol. 146 (1962), 1009\u201312."},{"key":"22","doi-asserted-by":"publisher","unstructured":"[22] Melnikov, A. 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