The model theory of the field of reals with a subgroup of the unit circle
The model theory of the field of reals with a subgroup of the unit circle
复制标题
单位圆子群的实数域模型论
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
B. Zilber
中科院分区：
文献类型：
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作者：
O. Belegradek;B. Zilber
我们描述了实数域中的可定义集合，并通过单位圆 ? 中包含的复数的有限秩乘法群 Γ 的谓词来增强。该结构解释了商空间 ?/Г，对于 Г 无限循环，它与量子环面相关。每个可定义集合都被证明是存在可定义集合的布尔组合。我们为这种结构的理论给出了一套完整的公理。
We describe definable sets in the field of reals augmented by a predicate for a finite rank multiplicative group Γ of complex numbers contained in the unit circle ?. This structure interprets the quotient‐space ?/Γ which, for Γ infinite cyclic, is related to the quantum torus. Every definable set is proved to be a Boolean combination of existentially definable sets. We give a complete set of axioms for the theory of such a structure.