{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T15:51:43Z","timestamp":1649001103592},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"content-version":"unspecified","delay-in-days":61,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2018,6]]},"abstract":"Abstract<\/jats:title>We prove that for every uncountable cardinal \u03ba<\/jats:italic> such that \u03ba<\u03ba<\/jats:sup> = \u03ba, the quasi-order of embeddability on the \u03ba<\/jats:italic>-space of \u03ba<\/jats:italic>-sized graphs Borel reduces to the embeddability on the \u03ba<\/jats:italic>-space of \u03ba<\/jats:italic>-sized torsion-free abelian groups. Then we use the same techniques to prove that the former Borel reduces to the embeddability relation on the \u03ba<\/jats:italic>-space of \u03ba<\/jats:italic>-sized R<\/jats:italic>-modules, for every $\\mathbb{S}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-cotorsion-free ring R<\/jats:italic> of cardinality less than the continuum. As a consequence we get that all the previous are complete $\\Sigma _1^1$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> quasi-orders.<\/jats:p>","DOI":"10.1017\/jsl.2018.9","type":"journal-article","created":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T07:16:04Z","timestamp":1533107764000},"page":"703-716","source":"Crossref","is-referenced-by-count":0,"title":["THE COMPLEXITY OF THE EMBEDDABILITY RELATION BETWEEN TORSION-FREE ABELIAN GROUPS OF UNCOUNTABLE SIZE"],"prefix":"10.1017","volume":"83","author":[{"given":"FILIPPO","family":"CALDERONI","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,8,1]]},"reference":[{"key":"S0022481218000099_ref2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-37-00308-9"},{"key":"S0022481218000099_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2014.02.027"},{"key":"S0022481218000099_ref16","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-05-04005-5"},{"key":"S0022481218000099_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2013.05.006"},{"key":"S0022481218000099_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-19422-6"},{"key":"S0022481218000099_ref4","doi-asserted-by":"crossref","unstructured":"[4] Calderoni F. and Thomas S. , The bi-embeddability relation for countable abelian groups. Transactions of the American Mathematical Society, to appear.","DOI":"10.1090\/tran\/7513"},{"key":"S0022481218000099_ref12","doi-asserted-by":"publisher","DOI":"10.4064\/fm175-3-2"},{"key":"S0022481218000099_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/b98977"},{"key":"S0022481218000099_ref3","unstructured":"[3] Calderoni F. , Mildenberger H. , and Ros L. M. , Uncountable structures are not classifiable up to bi-embeddability, submitted."},{"key":"S0022481218000099_ref20","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-02-00409-5"},{"key":"S0022481218000099_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S0022481218000099_ref1","unstructured":"[1] Andretta A. and Ros L. M. , Classifying uncountable structures up to bi-embeddability, preprint, 2016, arXiv:1609.09292v1."},{"key":"S0022481218000099_ref5","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-13.1.687"},{"key":"S0022481218000099_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.06.007"},{"key":"S0022481218000099_ref7","article-title":"Generalized descriptive set theory and classification theory","volume":"230","author":"Friedman","year":"2014","journal-title":"Memoirs of the American Mathematical Society,"},{"key":"S0022481218000099_ref8","volume-title":"Infinite Abelian Groups. Vol. I","volume":"36","author":"Fuchs","year":"1970"},{"key":"S0022481218000099_ref11","doi-asserted-by":"publisher","DOI":"10.1515\/9783110218114"},{"key":"S0022481218000099_ref13","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201200063"},{"key":"S0022481218000099_ref14","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201500062"},{"key":"S0022481218000099_ref17","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1016\/j.apal.2013.06.018","article-title":"The descriptive set-theoretical complexity of the embeddability relation on models of large size","volume":"164","author":"Ros","year":"2013","journal-title":"Annals of Pure and Applied Logic"},{"key":"S0022481218000099_ref21","unstructured":"[21] Williams J. , Universal countable Borel quasi-orders, this Journal, vol. 79 (2014), no. 3, pp. 928\u2013954."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481218000099","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,14]],"date-time":"2019-04-14T16:28:20Z","timestamp":1555259300000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481218000099\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["S0022481218000099"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2018.9","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6]]}}}