{"paper":{"title":"Characterizing finitary functions over non-archimedean RCFs via a topological definition of OVF-integrality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yoav Yaffe","submitted_at":"2011-03-09T20:57:27Z","abstract_excerpt":"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 associate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1873","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}