{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T18:27:32Z","timestamp":1757701652850},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2017,6]]},"abstract":"<jats:p>In [E.\u00a0Hrushovski, D.\u00a0Palac\u00edn and A.\u00a0Pillay, On the canonical base property, Selecta Math. (N.S.) 19(4) (2013) 865\u2013877], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that [Formula: see text] has the canonical base property in a strong form; \u201cinternality to\u201d being replaced by \u201calgebraicity in\u201d. In the current paper, we give a reasonably robust definition of the \u201cstrong canonical base property\u201d in a rather more general finite rank context than [E.\u00a0Hrushovski, D.\u00a0Palac\u00edn and A.\u00a0Pillay, On the canonical base property, Selecta Math. (N.S.) 19(4) (2013) 865\u2013877], and prove its equivalence with rigidity of the relevant definable Galois groups. The new direction is an elaboration on the old result that [Formula: see text]-based groups are rigid.<\/jats:p>","DOI":"10.1142\/s0219061317500027","type":"journal-article","created":{"date-parts":[[2017,3,21]],"date-time":"2017-03-21T07:11:03Z","timestamp":1490080263000},"page":"1750002","source":"Crossref","is-referenced-by-count":3,"title":["On definable Galois groups and the strong canonical base property"],"prefix":"10.1142","volume":"17","author":[{"given":"Daniel","family":"Palac\u00edn","sequence":"first","affiliation":[{"name":"Universit\u00e4t M\u00fcnster, Institut f\u00fcr Mathematische Logik, und Grundlagenforschung, Einsteinstrasse 62, 48149 M\u00fcnster, Germany"}]},{"given":"Anand","family":"Pillay","sequence":"additional","affiliation":[{"name":"University of Notre Dame, Departament of Mathematics, 281 Hurley Hall, Notre Dame, IN 46556, USA"}]}],"member":"219","published-online":{"date-parts":[[2017,3,21]]},"reference":[{"issue":"3","key":"S0219061317500027BIB001","first-page":"34","volume":"21","author":"Chatzidakis Z.","year":"2012","journal-title":"Confluentes Math."},{"key":"S0219061317500027BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s00029-013-0129-3"},{"key":"S0219061317500027BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(09)70556-7"},{"issue":"3","key":"S0219061317500027BIB004","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1215\/ijm\/1254403721","volume":"52","author":"Moosa R.","year":"2008","journal-title":"Illinois J. Math."},{"key":"S0219061317500027BIB005","doi-asserted-by":"publisher","DOI":"10.2178\/jsl.7802080"},{"key":"S0219061317500027BIB006","doi-asserted-by":"publisher","DOI":"10.4064\/fm224-1-3"},{"key":"S0219061317500027BIB007","series-title":"Oxford Logic Guides","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534372.001.0001","volume-title":"Geometric Stability Theory.","volume":"32","author":"Pillay A.","year":"1996"},{"key":"S0219061317500027BIB009","doi-asserted-by":"publisher","DOI":"10.4064\/fm174-2-3"},{"key":"S0219061317500027BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00029-003-0339-1"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061317500027","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T04:25:57Z","timestamp":1719116757000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061317500027"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,21]]},"references-count":9,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2017,2,2]]},"published-print":{"date-parts":[[2017,6]]}},"alternative-id":["10.1142\/S0219061317500027"],"URL":"https:\/\/doi.org\/10.1142\/s0219061317500027","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,21]]}}}