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arXiv · 1103.1873

Characterizing finitary functions over non-archimedean RCFs via a topological definition of OVF-integrality

Yoav Yaffe
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Abstract

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.

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Yoav Yaffe. 2011-03-13. Characterizing finitary functions over non-archimedean RCFs via a topological definition of OVF-integrality. https://arxiv.org/abs/1103.1873

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