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Under certain assumptions on the residue field, we prove quantifier elimination first in the pure module language, then in that language augmented with a chain of additive subgroups, and finally in a two-sorted language with a valuation map. We apply quantifier elimination to prove that these structures do not have the independence property.<\/jats:p>","DOI":"10.2178\/jsl\/1278682213","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T13:30:45Z","timestamp":1278682245000},"page":"1007-1034","source":"Crossref","is-referenced-by-count":3,"title":["Quantifier elimination in valued Ore modules"],"prefix":"10.1017","volume":"75","author":[{"given":"Luc","family":"B\u00e9lair","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7oise","family":"Point","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002516_ref029","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0099397"},{"key":"S0022481200002516_ref028","first-page":"323","volume-title":"Valuation theory and its applications, Vol. II (proceedings of the first international conference on valuation theory, saskatoon 1999)","volume":"33","author":"Scanlon","year":"2003"},{"key":"S0022481200002516_ref027","unstructured":"Rohwer T. , Valued difference fields as modules over twisted polynomial rings, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2003."},{"key":"S0022481200002516_ref026","first-page":"123","article-title":"Differential equations over valued fields (and more)","volume":"576","author":"Priess-Crampe","year":"2004","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"key":"S0022481200002516_ref025","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600562"},{"key":"S0022481200002516_ref023","doi-asserted-by":"crossref","first-page":"341","DOI":"10.36045\/bbms\/1126195339","article-title":"Quelques remarques concernant la th\u00e9orie des corps ordonn\u00e9s diff\u00e9rentiellement clos","volume":"12","author":"Michaux","year":"2005","journal-title":"Bulletin of the Belgian Mathematical Society. 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