特征为零的代数闭域的乘法群的覆盖
Covers of the multiplicative group of an algebraically closed field of characteristic zero
摘要：
我们研究的普遍覆盖的复杂的一维环面作为一个模型理论的结构，在自然语言。我们还考虑了特征为零的代数闭域上一维环面的抽象覆盖。主要结果表明，结构可以描述唯一的同构由一个简单的（非一阶）的句子，给定一个固定的不可数基数的基础领域。证明减少到循环伽罗瓦扩展的库默尔理论在一些，不一定是非线性生成的领域。
英文摘要：
We study the universal cover of the complex one-dimensional torus as a model-theoretic structure in a natural language. We consider also abstract covers of one-dimensional tori over algebraically closed fields of characteristic zero. The main result states that the structures can be described uniquely up to isomorphism by a simple (non-first order) sentence, given a fixed uncountable cardinality of the underlying field. The proof reduces to the Kummer theory of cyclic Galois extensions over some, not necessarily finitely generated fields.
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