4 papers
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…
Transition maps at non-resonant hyperbolic singularities are o-minimal
Tobias Kaiser, Jean-Philippe Rolin, Patrick Speissegger
We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field X and any isolated, non-resonant hyperbolic singu…
An ordered structure of rank two related to Dulac's problem
Alf Dolich, Patrick Speissegger
For a vector field F on the Euclidean plane we construct, under certain assumptions on F, an ordered model-theoretic structure associated to the flow of F. We do this in such a way…
The Pfaffian closure on an o-minimal structure
Patrick Speissegger
Every o-minimal expansion R-tilde of the real field has an o-minimal expansion P(R-tilde) in which the solutions to Pfaffian equations with definable C^1 coefficients are definable…