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Lectures on the Model Theory of Valued Fields

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Model Theory in Algebra, Analysis and Arithmetic

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2111))

Abstract

The subject originates in the 1950s with Abraham Robinson when he established the model completeness of the theory of algebraically closed valued fields. In the 1960s Ax & Kochen and, independently, Ershov, proved a remarkable theorem on henselian valued fields, with applications to p-adic number theory. These results and their refinements and extensions remain important in more recent developments like motivic integration.

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Notes

  1. 1.

    One should of course regard \(\mathcal{L}_{\text{r}}\) and \(\mathcal{L}_{\text{v}}\) as disjoint.

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  1. Department of Mathematics, University of Illinois, Urbana, IL, USA

    Lou van den Dries

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van den Dries, L. (2014). Lectures on the Model Theory of Valued Fields. In: Model Theory in Algebra, Analysis and Arithmetic. Lecture Notes in Mathematics(), vol 2111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54936-6_4

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