论文标题
非免费组中的非$ \ forall $ - 综合性
Non-$\forall$-homogeneity in free groups
论文作者
论文摘要
我们证明，有限排名至少3或可计数等级的非亚伯利亚自由群体不是$ \ forall $ - 均匀的。我们回答了来自Kharlampovich，Myasnikov和Sklinos的三个公开问题，涉及免费组，有限生成的基本免费团体和非亚伯限制组是否形成了特殊类型的Fraïssé课程，其中嵌入必须保留$ \ forall $ -formulas。我们还提供了有趣的非最佳生成基本免费组的有趣示例。
We prove that non-abelian free groups of finite rank at least 3 or of countable rank are not $\forall$-homogeneous. We answer three open questions from Kharlampovich, Myasnikov, and Sklinos regarding whether free groups, finitely generated elementary free groups, and non-abelian limit groups form special kinds of Fraïssé classes in which embeddings must preserve $\forall$-formulas. We also provide interesting examples of countable non-finitely generated elementary free groups.
