A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions

Abstract

Let $⟨K,\nu ⟩$ be a real closed valued field, and let $S\subseteq K^n$ be an open semi-algebraic set. Using tools from model theory, we find an algebraic characterization of rational functions which admit, on $S$, only values in the valuation ring. We use this result to deduce a criterion for a rational function to be bounded on an open semi algebraic subset of some irreducible variety over a real closed field or over an ordered field which is dense in its real closure.

arXiv commentAccepted to publication in Communications in Algebra

References in corpus (1)

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

Cited by in corpus (1)

• Positivstellensätze for semi-algebraic sets in real closed valued fields