代数闭值域中的稳定控制与独立性
Stable domination and independence in algebraically closed valued fields
摘要：
我们试图创建一个代数闭值域（ACVF）的类型的模型理论分析的工具。我们给出的证据表明，一个概念的“稳定部分的统治”起着关键作用。在第一部分，我们发展了一个稳定支配类型的一般理论，表明它们享有一个优秀的独立性理论，以及可定义类型和可定义函数芽的理论。在第二部分中，我们证明了一般理论适用于ACVF。在一个足够丰富的基础上，我们表明，每一种类型是稳定的主导其形象的价值组。对于任何基上的不变类型，稳定控制与“与值群正交”的自然概念相一致。我们还调查了其他独立的概念，并表明，他们都同意，并且表现良好，稳定主导的类型。其中之一是用来表明每个类型都可以扩展到一个不变类型;可定义类型是稠密的。这类工作大部分需要使用虚元素。我们还证明了在合理的基上存在素模型，可能包括元数。
英文摘要：
We seek to create tools for a model-theoretic analysis of types in algebraically closed valued fields (ACVF). We give evidence to show that a notion of 'domination by stable part' plays a key role. In Part A, we develop a general theory of stably dominated types, showing they enjoy an excellent independence theory, as well as a theory of definable types and germs of definable functions. In Part B, we show that the general theory applies to ACVF. Over a sufficiently rich base, we show that every type is stably dominated over its image in the value group. For invariant types over any base, stable domination coincides with a natural notion of `orthogonality to the value group'. We also investigate other notions of independence, and show that they all agree, and are well-behaved, for stably dominated types. One of these is used to show that every type extends to an invariant type; definable types are dense. Much of this work requires the use of imaginary elements. We also show existence of prime models over reasonable bases, possibly including imaginaries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
