论文标题
真实封闭场和强界结构的添加添加材料
Additive reducts of real closed fields and strongly bounded structures
论文作者
论文摘要
考虑到一个真正的封闭场$ r $，我们确定了$ r $的四个适当还原，从而扩展了基础（无序）$ r $ $ - 矢量空间结构。对于这个定理，我们引入了一个新的概念，该概念是线性有序结构的强大还原： 线性有序结构$ \ langle r; <，\ cdots \ rangle $的还原$ \数学m $称为\ emph {强限制}，如果每个$ \ Mathcal m $ -definable of $ r $ of $ r $都限制在$ r $中。我们研究了O-最低结构的强限制添加性还原，作为推论证明了上述定理对实际闭合场的添加性还原。
Given a real closed field $R$, we identify exactly four proper reducts of $R$ which expand the underlying (unordered) $R$-vector space structure. Towards this theorem we introduce a new notion, of strongly bounded reducts of linearly ordered structures: A reduct $\mathcal M$ of a linearly ordered structure $\langle R;<,\cdots\rangle $ is called \emph{strongly bounded} if every $\mathcal M$-definable subset of $R$ is either bounded or co-bounded in $R$. We investigate strongly bounded additive reducts of o-minimal structures and as a corollary prove the above theorem on additive reducts of real closed fields.
