Définissabilité avec paramètres extérieurs dans $\textbf {Q}_ p$ et $\textbf {R}$
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- by Françoise Delon
- Proc. Amer. Math. Soc. 106 (1989), 193-198
- DOI: https://doi.org/10.1090/S0002-9939-1989-0953003-8
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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
- F. Delon, Quelques propriétés des corps valués en théorie des modèles, thèse d’état, Paris VII, 1982.
- Lou van den Dries, Tarski’s problem and Pfaffian functions, Logic colloquium ’84 (Manchester, 1984) Stud. Logic Found. Math., vol. 120, North-Holland, Amsterdam, 1986, pp. 59–90. MR 861419, DOI 10.1016/S0049-237X(08)70457-9
- Angus Macintyre, On definable subsets of $p$-adic fields, J. Symbolic Logic 41 (1976), no. 3, 605–610. MR 485335, DOI 10.2307/2272038 —, Twenty years of $p$-adic model theory, in Logic Colloquium ’84, cité supra. D. Marker et C. Steinhorn, Definable types in $0$-minimal theories, preprint.
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- 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