The real field with the rational points of an elliptic curve

GÜNAYDIN, AYHAN; Hieronymi, Philipp

doi:10.4064/fm211-1-2

The real field with the rational points of an elliptic curve

GÜNAYDIN A., Hieronymi P.

Fundamenta Mathematicae, cilt.211, sa.1, ss.15-40, 2011 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 211 Sayı: 1
Basım Tarihi: 2011
Doi Numarası: 10.4064/fm211-1-2
Dergi Adı: Fundamenta Mathematicae
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.15-40
Anahtar Kelimeler: Definable set, Elliptic curve, Open core, Real field
Boğaziçi Üniversitesi Adresli: Evet

Özet

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. © Instytut Matematyczny PAN, 2011.