{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:33:00Z","timestamp":1747150380578,"version":"3.40.5"},"reference-count":14,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2023,9,5]],"date-time":"2023-09-05T00:00:00Z","timestamp":1693872000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and by Ben Yaacov, Doucha, Nies, and Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach\u2010Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of two\u2010sorted structures that witness approximate isomorphism. As an application, we show that the theory of any \u2010tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson\u00a0[8].<\/jats:p>","DOI":"10.1002\/malq.202200076","type":"journal-article","created":{"date-parts":[[2023,9,5]],"date-time":"2023-09-05T11:06:29Z","timestamp":1693911989000},"page":"482-507","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Approximate isomorphism of metric structures"],"prefix":"10.1002","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9269-3446","authenticated-orcid":false,"given":"James E.","family":"Hanson","sequence":"first","affiliation":[{"name":"Department of Mathematics University of Maryland USA"}]}],"member":"311","published-online":{"date-parts":[[2023,9,5]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061308000737"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061308000762"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.4115\/jla.2013.5.8"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2014-11956-3"},{"key":"e_1_2_9_6_1","series-title":"London Mathematical Society Lecture Note Series Vol. 2","first-page":"315","volume-title":"Model theory for metric structures","author":"Yaacov I. Ben","year":"2008"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2017.07.021"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/033"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.4115\/jla.2020.12.3"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061322500143"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2017.66.6019"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2022.103204"},{"key":"e_1_2_9_13_1","first-page":"77","volume-title":"Models, Algebras, and Proofs","author":"Iovino J.","year":"1998"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01075458"},{"key":"e_1_2_9_15_1","unstructured":"H.Tellez Contributions to model theory of metric structures Ph.D. thesis (University of Illinois at Urbana\u2010Champaign 2010)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.202200076","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T10:58:15Z","timestamp":1702983495000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.202200076"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,5]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["10.1002\/malq.202200076"],"URL":"https:\/\/doi.org\/10.1002\/malq.202200076","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[2023,9,5]]},"assertion":[{"value":"2022-12-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-07-31","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-09-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}