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Définissabilité avec paramètres extérieurs dans $ {\bf Q}\sb p$ et $ {\bf R}$


Author: Françoise Delon
Journal: Proc. Amer. Math. Soc. 106 (1989), 193-198
MSC: Primary 03C40; Secondary 03C60, 12L12
DOI: https://doi.org/10.1090/S0002-9939-1989-0953003-8
MathSciNet review: 953003
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Abstract: Let $ N$ be an elementary extension of the field $ {{\mathbf{Q}}_p}$ and $ A$ a definable subset of $ {N^n}$. Then $ A \cap {\mathbf{Q}}_p^n$ is definable in $ {{\mathbf{Q}}_p}$.


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

  • [D] F. Delon, Quelques propriétés des corps valués en théorie des modèles, thèse d'état, Paris VII, 1982.
  • [Dr] L. van den Dries, Tarski's problem and Pfaffian functions, in Logic Colloquium '84, Paris, Wilkie and Wilmers (ed.), North-Holland, Amsterdam 1986. MR 861419 (88f:03025)
  • [Mi1] A. Macintyre, On definable subsets of $ p$-adic fields, JSL 41 (1976), 605-610. MR 0485335 (58:5182)
  • [Mi2] -, Twenty years of $ p$-adic model theory, in Logic Colloquium '84, cité supra.
  • [MS] D. Marker et C. Steinhorn, Definable types in 0-minimal theories, preprint.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0953003-8
Keywords: Definable subset, analogy between $ {\mathbf{R}}$ and $ {{\mathbf{Q}}_p}$
Article copyright: © Copyright 1989 American Mathematical Society

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