具有标准零件图的O-极小域

摘要：

设R是O-极小域，V是具有剩余域k和标准部分（剩余）映射st的真凸子环：V \to k.设k_{ind}是k通过R中可定义关系的标准部分的展开。本文研究了k_{ind}中的可定义集和（R，V）上蕴含k_{ind}的o-极小性的条件.我们还证明了，如果R是Ω饱和的，V是R中有理数的凸包，那么在k_{ind}中可定义的集合恰好是在（R，V）中可定义的集合的标准部分.

英文摘要：

Let R be an o-minimal field and V a proper convex subring with residue field k and standard part (residue) map st: V \to k. Let k_{ind} be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in k_{ind} and conditions on (R,V) which imply o-minimality of k_{ind}. We also show that if R is omega-saturated and V is the convex hull of the rationals in R, then the sets definable in k_{ind} are exactly the standard parts of the sets definable in (R,V).

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