11 citations · 49 across the 21 of their papers we have counts for
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math.LO2009★ 6 cited
The real field with an irrational power function and a dense multiplicative subgroup
Philipp Hieronymi
This paper provides a first example of a model theoretically well behaved structure consisting of a proper o-minimal expansion of the real field and a dense multiplicative subgroup…
math.LO2009★ 1 cited
Defining the set of integers in expansions of the real field by a closed discrete set
Philipp Hieronymi
Let D\subseteq \mathbb{R} be closed and discrete and f:D^n \to \mathbb{R} be such that f(D^n) is somewhere dense. We show that (\mathbb{R},+,\cdot,f) defines the set of integers. A…
math.LO2009★ 7 cited
The real field with the rational points of an elliptic curve
Ayhan Gunaydin, Philipp Hieronymi
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…