2 citations · 2 across the 4 of their papers we have counts for
6 papers
Connectedness in structures on the real numbers: o-minimality and undecidability
Alfred Dolich, Chris Miller, Alex Savatovsky +1
We initiate an investigation of structures on the set of real numbers having the property that path components of definable sets are definable. All o\nobreakdash-\hspace{0pt}minima…
Expansions of the real field by canonical products
Chris Miller, Patrick Speissegger
We consider expansions of o-minimal structures on the real field by collections of restrictions to the positive real line of the canonical Weierstrass products associated to sequen…
Points of bounded height on oscillatory sets
Georges Comte, Chris Miller
We show that transcendental curves in (not necessarily compact) have few rational points of bounded height provided that the curves are well behaved with respect to a…
Metric dimensions and tameness in expansions of the real field
Philipp Hieronymi, Chris Miller
For first-order expansions of the field of real numbers, nondefinability of the set of natural numbers is equivalent to equality of topological and Assouad dimension on images of c…
A dichotomy for expansions of the real field
Antongiulio Fornasiero, Philipp Hieronymi, Chris Miller
A dichotomy for expansions of the real field is established: Either the set of integers is definable or every nonempty bounded nowhere dense definable subset of the real numbers ha…
Expansions of the real field by open sets: definability versus interpretability
H. Friedman, K. Kurdyka, C. Miller +1
An open set U of the real numbers R is produced such that the expansion (R,+,x,U) of the real field by U defines a Borel isomorph of (R,+,x,N) but does not define N. It follows tha…