Differential forms in the model theory of differential fields

@article{Pierce2003DifferentialFI,
  title={Differential forms in the model theory of differential fields},
  author={David Pierce},
  journal={J. Symb. Log.},
  year={2003},
  volume={68},
  pages={923-945}
}
Fields of characteristic zero with several commuting derivations can be treated as fields equipped with a space of derivations that is closed under the Lie bracket. The existentially closed instances of such structures can then be given a coordinate-free characterization in terms of differential forms. The main tool for doing this is a generalization of the Frobenius Theorem of differential geometry. 
6 Citations
13 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 13 references

volume 15 of Fields Inst

  • Anand Pillay. Differential fields. In Lectures on algebr theory
  • Monogr., pages 1–45. Amer. Math. Soc., Providence…
  • 2002

Symbolic Logic

  • J Tracey McGrail. The model theory of differential f derivations.
  • 65(2):885–913,
  • 2000
2 Excerpts

Math

  • Zoé Chatzidakis, Ehud Hrushovski. Model theory of difference fields. Tra Amer
  • Soc., 351(8):2997–3071,
  • 1999
1 Excerpt

Algebra

  • David Pierce, J AnandPillay.Anoteontheaxiomsfordifferentiallyclose
  • 204(1):108–115,
  • 1998
1 Excerpt

Logic

  • Angus Macintyre. Generic automorphisms of fields. Ann. P Appl
  • 88(2-3):165– 180,
  • 1997

volume 166 of Graduate Texts in Mathematics

  • R. W. Sharpe. Differential geometry
  • Springer-Verlag, New York,
  • 1997

volume 32 of Oxford Logic Guides

  • Anand Pillay. Geometric stability theory
  • The Clarendon Press Oxford University Press, New…
  • 1996

Differential Equations

  • Joseph Johnson, Georg M. Reinhart, J LeeA.Rubel.Somecounterexamplestoseparationofvariab
  • 121(1):42–66,
  • 1995
1 Excerpt

volume 42 of Encyclopedia of Mathematics and its Applications

  • Wilfrid Hodges. Model theory
  • Cambridge University Press, Cambridge,
  • 1993

San Francisco

  • Nathan Jacobson. Basic algebra. II.W.H. Freeman, Co.
  • Calif.,
  • 1980

Similar Papers

Loading similar papers…