Mathematics – Logic
Scientific paper
2011-03-09
Mathematics
Logic
The term `Kochen topology' was replaced by `Kochen geometry'
Scientific paper
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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