1. Asymptotic theories of differential fields
- Author
-
Zoé Chatzidakis and Ehud Hrushovski
- Subjects
Class (set theory) ,Pure mathematics ,Asymptotic analysis ,Conjecture ,General Mathematics ,12H99 ,Mathematical analysis ,Undecidable problem ,Decidability ,Asymptotology ,Vector field ,Differential algebra ,12L12 ,03C60 ,Mathematics - Abstract
We relate the integrability of vector fields, and of the vanishing of $p$-torsion, to model-theoretic questions concerning separably closed fields, endowed canonically with a derivation. While each differential field $(F_p(t)^s,D_p)$ is known to be decidable, we show that the asymptotic theory of these fields as a class is undecidable in a strong sense. This precludes a geometric answer to certain generalizations of the Grothendieck-Katz conjecture.
- Published
- 2003