论文标题
一个可计数的通用扭转阿贝尔纯度群体
A countable universal torsion abelian group for purity
论文作者
论文摘要
我们表明，有一个可数的通用阿伯利安P组，即纯度，即可数的Abelian p-Group $ U $，使每个可数的Abelian P组纯粹纯粹嵌入$ U $中。这是为[FUC15]低于$ \aleph_Ω$提供完整解决方案5.1的完整解决方案所需的最后结果。我们介绍了$ \ aleph_0 $ - 均匀的均质P组，表明有一个通用的Abelian P组纯度，即$ \ aleph_0 $ strongrong-Strongronglongly均质，并且完全表征可算出的$ \ aleph_0 $ - aleph_0 $ stronglongy-stronglongy-stronglongy-stronglongy proups p-groups。
We show that there is a countable universal abelian p-group for purity, i.e., a countable abelian p-group $U$ such that every countable abelian p-group purely embeds in $U$. This is the last result needed to provide a complete solution to Problem 5.1 of [Fuc15] below $\aleph_ω$. We introduce $\aleph_0$-strongly homogeneous p-groups, show that there is a universal abelian p-group for purity which is $\aleph_0$-strongly homogeneous, and completely characterize the countable $\aleph_0$-strongly homogeneous p-groups.
