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Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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01 Jan 2003
6 citations
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6 citations
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TL;DR: In this paper, it was shown that the asymptotic theory of vector fields as a class is undecidable in a strong sense, which precludes a geometric answer to certain generalizations of the Grothendieck-Katz conjecture.
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.
6 citations