The real field with the rational points of an elliptic curve

Volume 211 / 2011

Ayhan Günaydın, Philipp Hieronymi Fundamenta Mathematicae 211 (2011), 15-40 MSC: 03C10, 03C64, 14H52, 11U09. DOI: 10.4064/fm211-1-2


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.


  • Ayhan GünaydınCentro de Matemática
    e Aplicações Fundamentais
    Av. Prof. Gama Pinto, 2
    1649-003 Lisboa, Portugal
  • Philipp HieronymiDepartment of Mathematics & Statistics
    McMaster University
    1280 Main Street West
    Hamilton, ON, L8S 4K1, Canada
    Department of Mathematics
    University of Illinois
    1409 W. Green Street
    Urbana, IL 61801, U.S.A.

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