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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Elementarily equivalent fields with inequivalent perfect closures


Author: Carlos R. Videla
Journal: Proc. Amer. Math. Soc. 99 (1987), 171-175
MSC: Primary 12L12; Secondary 03C60, 12F99
MathSciNet review: 866447
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Abstract: We give a counterexample to the following conjecture due to L. V. den Dries: Let $ F,L$ be two fields of characteristic $ p$. If $ F \equiv L$ then $ {F^1}/{p^\infty } \equiv {L^1}/{p^\infty }$.


References [Enhancements On Off] (What's this?)

  • [1] G. L. Cherlin, Definability in power series rings of nonzero characteristic, Models and sets (Aachen, 1983) Lecture Notes in Math., vol. 1103, Springer, Berlin, 1984, pp. 102–112. MR 775690 (86h:03059), http://dx.doi.org/10.1007/BFb0099383
  • [2] I. R. Shafarevich, Basic algebraic geometry, Springer Study Edition, Springer-Verlag, Berlin-New York, 1977. Translated from the Russian by K. A. Hirsch; Revised printing of Grundlehren der mathematischen Wissenschaften, Vol. 213, 1974. MR 0447223 (56 #5538)
  • [3] L. Van den Dries, Model theory of fields, Thesis, Utrecht 1978, Stellingen 4.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0866447-8
PII: S 0002-9939(1987)0866447-8
Keywords: Elementary equivalence, valuation, nonstandard model
Article copyright: © Copyright 1987 American Mathematical Society