论文标题
一个非polybound的绝对关闭$ 36 $ -Shelah Group
A non-polybounded absolutely closed $36$-Shelah group
论文作者
论文摘要
对于每一个无限的红衣主教$κ$，带有$κ^+= 2^κ$，我们构建了$ g $ g $ of MADINALITY $ | g | =κ^+$，以至于（i）$ g $是$ 36 $ -SHELAH，这意味着任何子集$ a \ a \ abletsee $ a \ a \ abletset $ a \ abletset $ a \ seteq g $ of Cardinatity of Cardinatity的$ a^{36} = g $ （ii）$ g $是绝对$ \ mathsf {t _ {\！1} s} $ - 封闭，$ \ mathsf {t _ {\！1} s} $ - 离散，这意味着对于每个同源性$ h：g \ to y $ to y $ to y $ h： （iii）$ g $在g：xc_1xc_2 in g：xc_1xc_2 \ cdots xc_n = e \} $的$ \ {x \ in g：xc_1xc_2 in g：c_1，c_2，c_2，c_2，\ cdots，c_n \ in G $中。
For every infinite cardinal $κ$ with $κ^+=2^κ$ we construct a group $G$ of cardinality $|G|=κ^+$ such that (i) $G$ is $36$-Shelah, which means that $A^{36}=G$ for any subset $A\subseteq G$ of cardinality $|A|=|G|$; (ii) $G$ is absolutely $\mathsf{T_{\!1}S}$-closed and projectively $\mathsf{T_{\!1}S}$-discrete, which means that for every homomorphism $h:G\to Y$ to a $T_1$ topological semigroup $Y$ the image $h[G]$ is a closed discrete subspace of $Y$, (iii) $G$ cannot be covered by finitely many algebraic subsets, i.e., subsets of the form $\{x\in G:xc_1xc_2\cdots xc_n=e\}$ for some $c_1,c_2,\cdots,c_n\in G$.
