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Preprint Number 311

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311. Yoav Yaffe
Characterizing finitary functions over non-archimedean RCFs via a topological definition of OVF-integrality

Submission date: 23 March 2011.


When R is a non-archimedean real closed field we say that a function f\in R(\bar{X}) is finitary at a point \bar{b}\in R^n if on some neighborhood of \bar{b} the defined values of f are in the finite part of R. In this note we give a characterization of rational functions which are finitary on a set defined by positivity and finiteness conditions. The main novel ingredient is a proof that OVF-integrality has a natural topological definition, which allows us to apply a known Ganzstellensatz for the relevant valuation. We also give some information about the Kochen geometry associated with OVF-integrality.

Mathematics Subject Classification: 03C60

Keywords and phrases: real closed valued fields, non-archimedean fields, Ganzstellensatz, integral radical, Kochen goemetry.

Full text arXiv: pdf, ps.

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