{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T19:41:50Z","timestamp":1694979710637},"reference-count":38,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2018,7,23]],"date-time":"2018-07-23T00:00:00Z","timestamp":1532304000000},"content-version":"vor","delay-in-days":22,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological fields, which encompasses ordered or <jats:italic>p<\/jats:italic>\u2010valued differential fields, we find a partial Galois correspondence and we show one cannot expect more in general. In the class of ordered differential fields, using elimination of imaginaries in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600098-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600098:malq201600098-math-0001\" \/>, we establish a relative Galois correspondence for relatively definable subgroups of the group of differential order automorphisms.<\/jats:p>","DOI":"10.1002\/malq.201600098","type":"journal-article","created":{"date-parts":[[2018,7,24]],"date-time":"2018-07-24T06:16:12Z","timestamp":1532412972000},"page":"155-169","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On differential Galois groups of strongly normal extensions"],"prefix":"10.1002","volume":"64","author":[{"given":"Quentin","family":"Brouette","sequence":"first","affiliation":[{"name":"D\u00e9partement de Math\u00e9matique (Le Pentagone) Universit\u00e9 de Mons 20 place du Parc 7000 Mons Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7oise","family":"Point","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Math\u00e9matique (Le Pentagone) Universit\u00e9 de Mons 20 place du Parc 7000 Mons Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,7,23]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.01.002"},{"key":"e_1_2_9_3_1","unstructured":"Q.Brouette Differential Algebra Ordered Fields and Model Theory Ph.D. thesis Universit\u00e9 de Mons (2015)."},{"key":"e_1_2_9_4_1","unstructured":"Q.BrouetteandF.Point Differential Galois theory in the class of formally real differential fields preprint (2014) arXiv 1404.3338v1."},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1980-034-2"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-015-1272-2"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2013.02.006"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2009.08.001"},{"issue":"2","key":"e_1_2_9_9_1","first-page":"173","article-title":"Groupoids, imaginaries and internal covers","volume":"36","author":"Hrushovski E.","year":"2012","journal-title":"J. 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