The real field with the rational points of an elliptic curve

Ayhan Günaydin; Philipp Hieronymi

doi:10.4064/fm211-1-2

The real field with the rational points of an elliptic curve

Ayhan Günaydin, Philipp Hieronymi

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	15-40
Number of pages	26
Journal	Fundamenta Mathematicae
Volume	211
Issue number	1
DOIs	https://doi.org/10.4064/fm211-1-2
State	Published - 2011
Externally published	Yes

Keywords

Definable set
Elliptic curve
Open core
Real field

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.4064/fm211-1-2

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KW - Elliptic curve

KW - Open core

KW - Real field

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The real field with the rational points of an elliptic curve

Abstract

Keywords

ASJC Scopus subject areas

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