{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:02:46Z","timestamp":1759147366512},"reference-count":18,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2018,12,17]],"date-time":"2018-12-17T00:00:00Z","timestamp":1545004800000},"content-version":"vor","delay-in-days":16,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["310737"],"award-info":[{"award-number":["310737"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,12]]},"abstract":"Abstract<\/jats:title>Let be a universal class with categorical in a regular with arbitrarily large models, and let be the class of all for which there is such that . We prove that is totally categorical (i.e., \u03be\u2010categorical for all ) and for . This result is partially stronger and partially weaker than a related result due to Vasey. In addition to small differences in our categoricity transfer results, we provide a shorter and simpler proof. In the end we prove the main theorem of this paper: the models of are essentially vector spaces (or trivial, i.e., disintegrated).<\/jats:p>","DOI":"10.1002\/malq.201700076","type":"journal-article","created":{"date-parts":[[2018,12,17]],"date-time":"2018-12-17T15:08:12Z","timestamp":1545059292000},"page":"464-477","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Categoricity and universal classes"],"prefix":"10.1002","volume":"64","author":[{"given":"Tapani","family":"Hyttinen","sequence":"first","affiliation":[{"name":"Department of Mathematics University of Helsinki P.O. 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