有值域和相关结构的区别
Distality in valued fields and related structures
摘要：
研究了值域及相关结构中远点扩张的存在性和远点性。特别地，我们刻画了一大类有序阿贝尔群的远端性，给出了henselian值域的AKE式刻画，并证明了域的某些扩展，例如，对数-指数跨系列的微分场，都是远端的。作为分析值域的一种新工具，我们对阿贝尔群的纯短正合列采用了相对量词消去法。
英文摘要：
We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian valued fields, and demonstrate that certain expansions of fields, e.g., the differential field of logarithmic-exponential transseries, are distal. As a new tool for analyzing valued fields we employ a relative quantifier elimination for pure short exact sequences of abelian groups.
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