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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
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 }$.

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  • [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,
  • [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
  • [3] L. Van den Dries, Model theory of fields, Thesis, Utrecht 1978, Stellingen 4.

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Keywords: Elementary equivalence, valuation, nonstandard model
Article copyright: © Copyright 1987 American Mathematical Society

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