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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
DOI: https://doi.org/10.1090/S0002-9939-1987-0866447-8
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. Cherlin, Definability in power series rings of nonzero characteristic models and sets, Lecture Notes in Math., vol. 1103, Springer-Verlag, Berlin and New York, 1984. MR 775690 (86h:03059)
  • [2] I. R. Shafarevich, Basic algebraic geometry, Springer-Verlag, New York, 1977. 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: https://doi.org/10.1090/S0002-9939-1987-0866447-8
Keywords: Elementary equivalence, valuation, nonstandard model
Article copyright: © Copyright 1987 American Mathematical Society

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