{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T05:38:04Z","timestamp":1740721084107,"version":"3.38.0"},"reference-count":22,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T00:00:00Z","timestamp":1289952000000},"content-version":"vor","delay-in-days":4338,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that there exists no sentence<jats:italic>F<\/jats:italic>of the language of rings with an extra binary predicat I<jats:sub>2<\/jats:sub>satisfying the following property: for every definable set<jats:italic>X<\/jats:italic>\u2286 \u2102<jats:sup>2<\/jats:sup>,<jats:italic>X<\/jats:italic>is connected if and only if (\u2102,<jats:italic>X<\/jats:italic>) \u22a7<jats:italic>F<\/jats:italic>, where<jats:italic>I<\/jats:italic><jats:sub>2<\/jats:sub>is interpreted by<jats:italic>X.<\/jats:italic>We conjecture that the same result holds for closed subset of \u2102<jats:sup>2<\/jats:sup>. We prove some results motivated by this conjecture.<\/jats:p>","DOI":"10.1002\/malq.19990450411","type":"journal-article","created":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T16:31:05Z","timestamp":1290011465000},"page":"533-550","source":"Crossref","is-referenced-by-count":7,"title":["Definability of Geometric Properties in Algebraically Closed Fields"],"prefix":"10.1002","volume":"45","author":[{"given":"Olivier","family":"Chapuis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pascal","family":"Koiran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,11,17]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90038-6"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"Basu S. An improved algorithm for quantifier elimination over real closed fields. In: 38th IEEE Symposium on Foundations of Computer Science1997 pp.56\u201365.","DOI":"10.1109\/SFCS.1997.646093"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/235809.235813"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/273865.273870"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"Benedikt M. andL.Libkin On the structure of queries in constraint query languages. In: 11th Annual IEEE Symposium on Logic in Computer Science New Brunswick NJ; IEEE Comput. Soc. Press Los Alamitos CA 1996 pp.25\u201334.","DOI":"10.1109\/LICS.1996.561300"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"Benedikt M. andL.Libkin Languages for relational databases over interpreted structures. 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