阿贝尔群中的三元组和
Sums of triples in Abelian groups
摘要：
出于在添加剂拉姆齐理论的问题，我们扩展Todorcevic的分区的三维组合立方体处理额外的三维物体。作为推论，我们得到，如果连续统假设失败，则对于每个大小为$\aleph_2$的阿贝尔群$G$，存在着色$c:G\rightarrow\mathbb Z$，使得对于每个不可数$X\subseteq G$和每个整数$k$，存在$X$的三个不同元素$x,y,z$，使得$c(x+y+z)=k$。
英文摘要：
Motivated by a problem in additive Ramsey theory, we extend Todorcevic's partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for every Abelian group $G$ of size $\aleph_2$, there exists a coloring $c:G\rightarrow\mathbb Z$ such that for every uncountable $X\subseteq G$ and every integer $k$, there are three distinct elements $x,y,z$ of $X$ such that $c(x+y+z)=k$.
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