半代数集的Ganzstellen定理和有理函数的有界性判据
A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions
摘要：
设$\langle K,ν\rangle$是实闭值域，$S\subseteq K^n$是开半代数集.利用模型论的工具，我们找到了有理函数的一个代数特征，它在$S$上只允许赋值环中的值。利用这个结果，我们得到了实闭域或实闭包稠密的序域上的有理函数在某个不可约簇的开半代数子集上有界的一个判别准则.
英文摘要：
Let $\langle K,ν\rangle$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
