## Journal of Symbolic Logic

### Separably closed fields with Hasse derivations

Martin Ziegler

#### Abstract

In \cite{MessmerW1995} Messmer and Wood proved quantifier elimination for separably closed fields of finite Ershov invariant $e$ equipped with a (certain) \Hde. We propose a variant of their theory, using a sequence of $e$ commuting \Hds. In contrast to \cite{MessmerW1995} our \Hds are iterative.

#### Article information

Source
J. Symbolic Logic, Volume 68, Issue 1 (2003), 311-318.

Dates
First available in Project Euclid: 21 February 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1045861515

Digital Object Identifier
doi:10.2178/jsl/1045861515

Mathematical Reviews number (MathSciNet)
MR1959321

Zentralblatt MATH identifier
1039.03031

#### Citation

Ziegler, Martin. Separably closed fields with Hasse derivations. J. Symbolic Logic 68 (2003), no. 1, 311--318. doi:10.2178/jsl/1045861515. https://projecteuclid.org/euclid.jsl/1045861515

#### References

• Françoise Delon Separably closed fields, Model theory and algebraic geometry, Lecture Notes in Mathematics, vol. 1696, Springer, Berlin,1998, pp. 143--176.
• Helmut Hasse and F. K. Schmidt Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper mit einer Unbestimmten, Journal für die Reine und Angewandte Mathematik, vol. 177 (1937), pp. 215--237.
• Hideyuki Matsumara Commutative ring theory, Cambridge University Press,1986.
• B. Heinrich Matzat Differential galois theory in positive characteristic, Lecture Notes, October 2001.
• Margit Messmer Some model theory of separably closed fields, Model theory of fields (D. Marker, M. Messmer, and A. Pillay, editors), Lecture Notes in Logic, vol. 5, Springer, Berlin,1996, pp. 135--152.
• Margit Messmer and Carol Wood Separably closed fields with higher derivations. I, Journal of Symbolic Logic, vol. 60 (1995), no. 3, pp. 898--910.
• Kôtaro Okugawa Basic properties of differential fields of an arbitrary characteristic and the Picard-Vessiot theory, Journal of Mathematics of Kyoto University, vol. 2 (1963), no. 3, pp. 294--322.
• Carol Wood Notes on the stability of separably closed fields, Journal of Symbolic Logic, vol. 44 (1979), no. 3, pp. 412--416.