论文标题
分类的涂鸦组的嵌入属性
The embedding property for sorted profinite groups
论文作者
论文摘要
我们研究分类的涂鸦组类别中的嵌入性能。我们介绍了分类嵌入属性（SEP）的概念，类似于涂鸦组的嵌入性质。我们表明，任何分类的涂鸦组都具有通用的sep覆盖。我们的证明为存在的普遍嵌入组的覆盖物提供了替代证明。我们的证明也适用于分类的涂鸦组的任何完整子类别，该类别在采用有限的商，纤维产品和倒数限制下关闭。 我们还引入了有限分类的嵌入属性（FSEP）较弱的概念，事实证明这与Sep相当。 FSEP的优点是能够用分类完整系统的一阶语言进行公理。使用此情况，我们表明，在假设类别的集合是可计数的，任何具有SEP的分类的涂鸦组都具有分类的完整系统。在这种情况下，作为副产品，我们获得了分类涂鸦群的通用sep覆盖的唯一性，该群体概括了涂鸦组的嵌入覆盖物的独特性。
We study the embedding property in the category of sorted profinite groups. We introduce a notion of the sorted embedding property (SEP), analogous to the embedding property for profinite groups. We show that any sorted profinite group has a universal SEP-cover. Our proof gives an alternative proof for the existence of a universal embedding cover of a profinite group. Also our proof works for any full subcategory of the sorted profinite groups, which is closed under taking finite quotients, fibre product, and inverse limit. We also introduce a weaker notion of finitely sorted embedding property (FSEP), and it turns out to be equivalent to SEP. The advantage of FSEP is to be able to be axiomatized in the first order language of sorted complete systems. Using this, we show that any sorted profinite group having SEP has the sorted complete system whose theory is $ω$-stable under the assumption that the set of sorts is countable. In this case, as a byproduct, we get the uniqueness of a universal SEP-cover of a sorted profinite group, which generalizes the uniqueness of an embedding cover of a profinite group.
