论文标题
公制有价值字段的大概AKE原理
An Approximate AKE Principle for Metric Valued Fields
论文作者
论文摘要
我们按照本·亚科夫（Ben Yaacov）的方法研究了连续逻辑中的度量值字段，从而在投影线给出的度量空间中工作。作为我们的主要结果，我们在此框架中获得了近似的Ax-Kochen-Ershov原理，从残基0和值组中完全描述了等效性0中的基本等效性。此外，我们表明，在任何特征中，指标有价值的差异领域的理论都不承认模型企业。这回答了本·亚科夫的问题。
We study metric valued fields in continuous logic, following Ben Yaacov's approach, thus working in the metric space given by the projective line. As our main result, we obtain an approximate Ax-Kochen-Ershov principle in this framework, completely describing elementary equivalence in equicharacteristic 0 in terms of the residue field and value group. Moreover, we show that, in any characteristic, the theory of metric valued difference fields does not admit a model-companion. This answers a question of Ben Yaacov.
