The real field with the rational points of an elliptic curve

• Autorzy: Ayhan Günaydın , Philipp Hieronymi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03C10: Quantifier elimination, model completeness and related topics
• 03C64: Model theory of ordered structures; o-minimality
• 11U09: Model theory
• 14H52: Elliptic curves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 211
• Numer: 1
• Strony: 15-40

Daty

wydano

2011

Twórcy

autor

Ayhan Günaydın

• Centro de Matemática, e Aplicações Fundamentais, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal

autor

Philipp Hieronymi

• Department 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.

Identyfikatory

DOI

10.4064/fm211-1-2