Geodesic
The real field with the rational points of an elliptic curve
Ayhan Günaydın 1   ; Philipp Hieronymi 2
1 Centro de Matemática e Aplicações Fundamentais Av. Prof. Gama Pinto, 2 1649-003 Lisboa, Portugal
2 Department of Mathematics & Statistics McMaster University 1280 Main Street West Hamilton, ON, L8S 4K1, Canada and Department of Mathematics University of Illinois 1409 W. Green Street Urbana, IL 61801, U.S.A.
Fundamenta Mathematicae, Tome 211 (2011) no. 1, pp. 15-40 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets definable in that structure are semialgebraic.
DOI : 10.4064/fm211-1-2
Keywords: consider expansion real field group rational points elliptic curve rational numbers prove completeness result followed quantifier elimination result moreover sets definable structure semialgebraic

Ayhan Günaydın  1   ; Philipp Hieronymi  2

1 Centro de Matemática e Aplicações Fundamentais Av. Prof. Gama Pinto, 2 1649-003 Lisboa, Portugal
2 Department of Mathematics & Statistics McMaster University 1280 Main Street West Hamilton, ON, L8S 4K1, Canada and Department of Mathematics University of Illinois 1409 W. Green Street Urbana, IL 61801, U.S.A. 
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Ayhan Günaydın; Philipp Hieronymi. The real field with the rational points of an elliptic curve. Fundamenta Mathematicae, Tome 211 (2011) no. 1, pp. 15-40. doi: 10.4064/fm211-1-2

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