{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:22:55Z","timestamp":1740108175916,"version":"3.37.3"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2016,9,12]],"date-time":"2016-09-12T00:00:00Z","timestamp":1473638400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2016,11]]},"DOI":"10.1007\/s00153-016-0506-7","type":"journal-article","created":{"date-parts":[[2016,9,12]],"date-time":"2016-09-12T00:20:03Z","timestamp":1473639603000},"page":"939-954","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The classification of $${\\mathbb {Z}}_p$$ Z p -modules with partial decomposition bases in $$L_{\\infty \\omega }$$ L \u221e \u03c9"],"prefix":"10.1007","volume":"55","author":[{"given":"Carol","family":"Jacoby","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0229-8624","authenticated-orcid":false,"given":"Peter","family":"Loth","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,9,12]]},"reference":[{"key":"506_CR1","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1215\/S0012-7094-37-00308-9","volume":"3","author":"R Baer","year":"1937","unstructured":"Baer, R.: Abelian groups without elements of finite order. Duke Math. J. 3, 68\u2013122 (1937)","journal-title":"Duke Math. J."},{"key":"506_CR2","first-page":"2","volume-title":"Studies in Model Theory. Studies in Mathematics","author":"J Barwise","year":"1973","unstructured":"Barwise, J.: Back and forth through infinitary logic. In: Morley, M.D. (ed.) Studies in Model Theory. Studies in Mathematics, p. 2. Mathematical Association of America, Washington (1973)"},{"key":"506_CR3","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0003-4843(70)90006-9","volume":"2","author":"J Barwise","year":"1970","unstructured":"Barwise, J., Eklof, P.: Infinitary properties of abelian torsion groups. Ann. Math. Log. 2, 25\u201368 (1970)","journal-title":"Ann. Math. Log."},{"key":"506_CR4","volume-title":"Infinite Abelian Groups","author":"L Fuchs","year":"1973","unstructured":"Fuchs, L.: Infinite Abelian Groups, vol. II. Academic Press, New York (1973)"},{"key":"506_CR5","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1216\/JCA-2011-3-3-321","volume":"3","author":"R G\u00f6bel","year":"2011","unstructured":"G\u00f6bel, R., Leistner, K., Loth, P., Str\u00fcngmann, L.: Infinitary equivalence of $$\\mathbb{Z}_p$$ Z p -modules with nice decomposition bases. J. Comm. Algebra 3, 321\u2013348 (2011)","journal-title":"J. Comm. Algebra"},{"key":"506_CR6","unstructured":"Hill, P.: On the classification of abelian groups, Preprint (1967)"},{"key":"506_CR7","doi-asserted-by":"crossref","unstructured":"Hunter, R., Richman, F.: Global Warfield groups. Trans. Am. Math. Soc. 266(1), 555\u2013572 (1981)","DOI":"10.1090\/S0002-9947-1981-0617551-X"},{"key":"506_CR8","doi-asserted-by":"crossref","unstructured":"Hunter, R., Richman, F., Walker, E.: Warfield modules. In: Abelian Group Theory, Lecture Notes in Mathematics, vol. 616, pp. 87\u2013123. Springer (1977)","DOI":"10.1007\/BFb0068191"},{"key":"506_CR9","unstructured":"Jacoby, C.: The classification in $$L_{\\infty \\omega }$$ L \u221e \u03c9 of groups with partial decomposition bases. Ph.D. thesis, University of California, Irvine (1980), revised version (2010)"},{"key":"506_CR10","doi-asserted-by":"crossref","unstructured":"Jacoby, C.: Undefinability of local Warfield groups in $$L_{\\infty \\omega }$$ L \u221e \u03c9 . In: Groups and Model Theory: A Conference in Honor of R\u00fcdiger G\u00f6bel\u2019s 70th Birthday, Contemp. Math., vol. 576, pp. 151\u2013162. American Mathematical Society, Providence, RI (2012)","DOI":"10.1090\/conm\/576\/11347"},{"key":"506_CR11","doi-asserted-by":"crossref","unstructured":"Jacoby, C. and Loth, P.: Abelian groups with partial decomposition bases in $$L_{\\infty \\omega }^\\delta $$ L \u221e \u03c9 \u03b4 , Part II. In: Groups and Model Theory: A Conference in Honor of R\u00fcdiger G\u00f6bel\u2019s 70th Birthday, Contemp. Math., vol. 576, pp. 177\u2013185. American Mathematical Society, Providence, RI (2012)","DOI":"10.1090\/conm\/576\/11348"},{"issue":"4","key":"506_CR12","first-page":"1007","volume":"40","author":"C Jacoby","year":"2014","unstructured":"Jacoby, C., Loth, P.: $$\\mathbb{Z}_p$$ Z p -modules with partial decomposition bases in $$L_{\\infty \\omega }^\\delta $$ L \u221e \u03c9 \u03b4 . Houst. J. Math. 40(4), 1007\u20131019 (2014)","journal-title":"Houst. J. Math."},{"key":"506_CR13","doi-asserted-by":"crossref","first-page":"4333","DOI":"10.1080\/00927872.2013.810747","volume":"42","author":"C Jacoby","year":"2014","unstructured":"Jacoby, C., Loth, P.: Partial decomposition bases and Warfield modules. Comm. Algebra 42, 4333\u20134349 (2014)","journal-title":"Comm. Algebra"},{"key":"506_CR14","doi-asserted-by":"crossref","unstructured":"Jacoby, C., Loth, P.: Partial decomposition bases and global Warfield groups, Comm. Algebra 44, 3262\u20133277 (2016)","DOI":"10.1080\/00927872.2015.1085547"},{"key":"506_CR15","unstructured":"Jacoby, C., Loth, P.: The classification of infinite abelian groups with partial decomposition bases in $$L_{\\infty \\omega }$$ L \u221e \u03c9 Rocky Mountain J. Math. (to appear)"},{"key":"506_CR16","doi-asserted-by":"crossref","unstructured":"Jacoby, C., Leistner, K., Loth, P., Str\u00fcngmann, L.: Abelian groups with partial decomposition bases in $$L_{\\infty \\omega }^\\delta $$ L \u221e \u03c9 \u03b4 , Part I. In: Groups and Model Theory: A Conference in Honor of R\u00fcdiger G\u00f6bel\u2019s 70th Birthday, Contemp. Math., vol. 576, pp. 163\u2013175. American Mathematical Society, Providence, RI (2012)","DOI":"10.1090\/conm\/576\/11349"},{"key":"506_CR17","volume-title":"Infinite Abelian Groups","author":"I Kaplansky","year":"1968","unstructured":"Kaplansky, I.: Infinite Abelian Groups. University of Michigan Press, Ann Arbor (1968)"},{"key":"506_CR18","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1090\/S0002-9947-1952-0046349-0","volume":"72","author":"I Kaplansky","year":"1952","unstructured":"Kaplansky, I.: Modules over Dedekind rings and valuation rings. Trans. Am. Math. Soc. 72, 327\u2013340 (1952)","journal-title":"Trans. Am. Math. Soc."},{"key":"506_CR19","first-page":"407","volume-title":"The Theory of Models","author":"C Karp","year":"1965","unstructured":"Karp, C.: Finite quantification equivalence. In: Addison, J.W., Henkin, L., Tarski, A. (eds.) The Theory of Models, pp. 407\u2013412. North-Holland, Amsterdam (1965)"},{"key":"506_CR20","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1007\/BF01135839","volume":"101","author":"R Nunke","year":"1967","unstructured":"Nunke, R.: Homology and direct sums of countable abelian groups. Math. Zeit 101, 182\u2013212 (1967)","journal-title":"Math. Zeit"},{"key":"506_CR21","doi-asserted-by":"crossref","unstructured":"Richman, F.: A guide to valuated groups. In: Abelian Group Theory. Lecture Notes in Mathematics, vol. 616, pp. 73\u201386. Springer (1977)","DOI":"10.1007\/BFb0068190"},{"key":"506_CR22","doi-asserted-by":"crossref","unstructured":"Stanton, R. O.: Decomposition bases and Ulm\u2019s Theorem. In: Abelian Group Theory. Lecture Notes in Mathematics, vol. 616, pp. 39\u201356. Springer (1977)","DOI":"10.1007\/BFb0068188"},{"key":"506_CR23","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1007\/BF01448919","volume":"107","author":"H Ulm","year":"1933","unstructured":"Ulm, H.: Zur Theorie der abzahlbar-unendlichen abelschen Gruppen. Math. Ann. 107, 774\u2013803 (1933)","journal-title":"Math. Ann."},{"key":"506_CR24","first-page":"33","volume":"222","author":"RB Warfield","year":"1976","unstructured":"Warfield, R.B.: Classification theory of abelian groups I, balanced projectives. Trans. Am. Math. Soc. 222, 33\u201363 (1976)","journal-title":"Trans. Am. Math. Soc."},{"key":"506_CR25","doi-asserted-by":"crossref","unstructured":"Warfield, R. B.: Classification theory of abelian groups II, local theory. Lecture Notes in Mathematics, vol. 874, pp. 322\u2013349. Springer (1981)","DOI":"10.1007\/BFb0090545"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-016-0506-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-016-0506-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-016-0506-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,13]],"date-time":"2019-09-13T07:07:55Z","timestamp":1568358475000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-016-0506-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,12]]},"references-count":25,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2016,11]]}},"alternative-id":["506"],"URL":"https:\/\/doi.org\/10.1007\/s00153-016-0506-7","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"type":"print","value":"0933-5846"},{"type":"electronic","value":"1432-0665"}],"subject":[],"published":{"date-parts":[[2016,9,12]]}}}