{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T07:10:26Z","timestamp":1698736226972},"reference-count":24,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2012,10,10]],"date-time":"2012-10-10T00:00:00Z","timestamp":1349827200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce new first\u2010order languages for the elementary <jats:italic>n<\/jats:italic>\u2010dimensional geometry and elementary <jats:italic>n<\/jats:italic>\u2010dimensional affine geometry (<jats:italic>n<\/jats:italic> \u2265 2), based on extending <jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathsf {FO}(\\beta ,\\equiv )$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-1.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content> and <jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathsf {FO}(\\beta )$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-2.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>, respectively, with new function symbols. Here, \u03b2 stands for the betweenness relation and \u2261 for the congruence relation. We show that the associated theories admit effective quantifier elimination.<\/jats:p>","DOI":"10.1002\/malq.201100095","type":"journal-article","created":{"date-parts":[[2012,10,10]],"date-time":"2012-10-10T10:32:46Z","timestamp":1349865166000},"page":"399-416","source":"Crossref","is-referenced-by-count":0,"title":["Quantifier elimination for elementary geometry and elementary affine geometry"],"prefix":"10.1002","volume":"58","author":[{"given":"Rafael","family":"Grimson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bart","family":"Kuijpers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Walied","family":"Othman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,10,10]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5587-4_7"},{"key":"e_1_2_10_3_1","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-33099-2","volume-title":"Algorithms in Real Algebraic Geometry, Algorithms and Computation in Mathematics Vol. 10","author":"Basu S.","year":"2006"},{"key":"e_1_2_10_4_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03718-8","volume-title":"Real Algebraic Geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete","author":"Bochnak J.","year":"1998"},{"key":"e_1_2_10_5_1","volume-title":"La G\u00e9om\u00e9trie","author":"Descartes R.","year":"1637"},{"key":"e_1_2_10_6_1","volume-title":"A mathematical introduction to logic","author":"Enderton H.","year":"2000"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1999.1630"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-22676-7"},{"key":"e_1_2_10_9_1","volume-title":"Grundlagen der Geometrie","author":"Hilbert D.","year":"1899"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04031-7"},{"key":"e_1_2_10_11_1","volume-title":"Model theory: an introduction, Graduate texts in mathematics Vol. 217","author":"Marker D.","year":"2002"},{"key":"e_1_2_10_12_1","first-page":"143","article-title":"Quantifier\u2010free axioms for constructive plane geometry","volume":"20","author":"Moler N.","year":"1968","journal-title":"Compos. 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