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A failure of quantifier elimination.

Angus Macintyre, David Marker (1997)

Revista Matemática de la Universidad Complutense de Madrid

We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.

The real field with the rational points of an elliptic curve

Ayhan Günaydın, Philipp Hieronymi (2011)

Fundamenta Mathematicae

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.

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