2009, English, Article edition: Model theoretic properties of metric valued fields Ben Yaacov, Itaï

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Physical Description
  • text
Published
  • HAL - CCSD
  • 2009
Language
  • English

Edition details

Title
  • Model theoretic properties of metric valued fields
Author
  • Ben Yaacov, Itaï
Published
  • HAL - CCSD
  • 2009
Physical Description
  • text
Subjects
Notes
  • We study model theoretic properties of valued fields (equipped with a real-valued multiplicative valuation), viewed as metric structures in continuous first order logic. For technical reasons we prefer to consider not the valued field $(K,|{\cdot}|)$ directly, but rather the associated projective spaces $K\bP^n$, as bounded metric structures. We show that the class of (projective spaces over) metric valued fields is elementary, with theory $MVF$, and that the projective spaces $\bP^n$ and $\bP^m$ are biïnterpretable for every $n,m \geq 1$. The theory $MVF$ admits a model completion $ACMVF$, the theory of algebraically closed metric valued fields (with a non trivial valuation). This theory is strictly stable, even up to perturbation. Similarly, we show that the theory of real closed metric valued fields, $RCMVF$, is the model companion of the theory of formally real metric valued fields, and that it is dependent.
  • HAL:hal-00407559, version 1
  • HAL:http:/​/​hal.archives-ouvertes.fr/​hal-00407559/​en/​
  • ARXIV:0907.4560
Language
  • English
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