论文标题
通过估值削减扩展的O最低结构的量化器消除
Quantifier elimination for o-minimal structures expanded by a valuational cut
论文作者
论文摘要
让$ r $是$ \ textrm {th}（r）$消除量词的语言的O小组的O小型扩展，而让$ c $成为$ r $估值的谓词。我们确定了一种暗示$ \ textrm {th}（r，c）$ r $的语言的量化器的条件，该语言是$ c $和少量常数扩展的，而$ \ textrm {th}（th}（r，c）$又暗示了它具有量化器消除和普遍轴承式的。例如，在$ c $是O-Minimal Field $ r $的凸点的情况下，该条件适用，其残留场是O-Minimal。
Let $R$ be an o-minimal expansion of a group in a language in which $\textrm{Th}(R)$ eliminates quantifiers, and let $C$ be a predicate for a valuational cut in $R$. We identify a condition that implies quantifier elimination for $\textrm{Th}(R,C)$ in the language of $R$ expanded by $C$ and a small number of constants, and which, in turn, is implied by $\textrm{Th}(R,C)$ having quantifier elimination and being universally axiomatizable. The condition applies for example in the case when $C$ is a convex subring of an o-minimal field $R$ and its residue field is o-minimal.
