The real field with the rational points of an elliptic curve

Ayhan Günaydin, Philipp Hieronymi

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)15-40
Number of pages26
JournalFundamenta Mathematicae
Volume211
Issue number1
DOIs
StatePublished - Jul 13 2011

Keywords

  • Definable set
  • Elliptic curve
  • Open core
  • Real field

ASJC Scopus subject areas

  • Algebra and Number Theory

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