自由群理论中的双曲塔与独立类集
Hyperbolic towers and independent generic sets in the theory of free groups
摘要：
我们使用双曲塔回答一些模型理论的问题，围绕一般类型的自由群理论。我们表明，所有的这一理论的生成模型实现的通用类型$p_0$，但有一个生成的模型省略了$p_0^{(2)}$。我们展示了一个生成的模型，其中有两个最大的独立集的实现的通用类型，具有不同的基数。我们还证明了齐次群的自由积不一定是齐次的。
英文摘要：
We use hyperbolic towers to answer some model theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type $p_0$, but that there is a finitely generated model which omits $p_0^{(2)}$. We exhibit a finitely generated model in which there are two maximal independent sets of realizations of the generic type which have different cardinalities. We also show that a free product of homogeneous groups is not necessarily homogeneous.
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