{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T05:19:09Z","timestamp":1767849549964,"version":"3.49.0"},"reference-count":3,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"NSF","award":["DMS-1700095"],"award-info":[{"award-number":["DMS-1700095"]}]},{"name":"NSF CAREER","award":["1945251"],"award-info":[{"award-number":["1945251"]}]},{"name":"ANR-DFG program GeoMod","award":["2100310201"],"award-info":[{"award-number":["2100310201"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:p> In this paper, it is shown that if [Formula: see text] is a complete type of Lascar rank at least\u00a02, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations [Formula: see text], [Formula: see text] such that p has a nonalgebraic forking extension over [Formula: see text]. Moreover, if A is contained in the field of constants then\u00a0p already has a nonalgebraic forking extension over [Formula: see text]. The results are also formulated in a more general setting. <\/jats:p>","DOI":"10.1142\/s0219061322500313","type":"journal-article","created":{"date-parts":[[2022,11,9]],"date-time":"2022-11-09T08:25:23Z","timestamp":1667982323000},"source":"Crossref","is-referenced-by-count":4,"title":["The degree of nonminimality is at most\u00a02"],"prefix":"10.1142","volume":"23","author":[{"given":"James","family":"Freitag","sequence":"first","affiliation":[{"name":"University of Illinois Chicago, Department of Mathematics, Statistics, and Computer Science, 851 S. Morgan Street, Chicago, IL, 60607-7045, USA"}]},{"given":"R\u00e9mi","family":"Jaoui","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 Blvd. du 11 Novembre 1918, 69622 Villeurbanne, France"}]},{"given":"Rahim","family":"Moosa","sequence":"additional","affiliation":[{"name":"University of Waterloo, Department of Pure Mathematics, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada"}]}],"member":"219","published-online":{"date-parts":[[2023,1,31]]},"reference":[{"key":"S0219061322500313BIB003","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1007\/s00222-022-01143-8","volume":"230","author":"Freitag J.","year":"2022","journal-title":"Invent. Math."},{"issue":"5","key":"S0219061322500313BIB005","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1007\/BF01207571","volume":"41","author":"Knop F.","year":"1983","journal-title":"Arch. der Math."},{"issue":"4","key":"S0219061322500313BIB006","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1007\/s00029-014-0150-1","volume":"20","author":"Moosa R.","year":"2014","journal-title":"Selecta Math."}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061322500313","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T08:23:47Z","timestamp":1687249427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219061322500313"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,31]]},"references-count":3,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["10.1142\/S0219061322500313"],"URL":"https:\/\/doi.org\/10.1142\/s0219061322500313","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,31]]},"article-number":"2250031"}}