论文标题
将许多定位枢机主教分开
Separating Many Localisation Cardinals on the Generalised Baire Space
论文作者
论文摘要
鉴于{}^κ$ in $κ$不可访问的Cofinal基本功能$ h \，我们认为，$ H $ localisation数字，即，$ H $ slaloms的主要基数最小的基数是，每个$κ$ -REAL都会在统治集合中进行稳定性。在Arxiv：1611.08140中证明，对于两个函数$ H $（身份函数和功率函数），主导的本地化数字可能会持续不同。我们将构建一个$κ$大小的功能$ h $及其相应的本地化数字，并使用$ {\ leq}κ$ - 支持辅助性具有辅助性的产物，迫使证明这些本地化编号的任何同时分配给在$κ$ $κ$上方的红衣主教的任何同时分配是一致的。这回答了Arxiv：1611.08140的一个公开问题。
Given a cofinal cardinal function $h\in{}^κκ$ for $κ$ inaccessible, we consider the dominating $h$-localisation number, that is, the least cardinality of a dominating set of $h$-slaloms such that every $κ$-real is localised by a slalom in the dominating set. It was proved in arXiv:1611.08140 that the dominating localisation numbers can be consistently different for two functions $h$ (the identity function and the power function). We will construct a $κ$-sized family of functions $h$ and their corresponding localisation numbers, and use a ${\leq}κ$-supported product of a cofinality-preserving forcing to prove that any simultaneous assignment of these localisation numbers to cardinals above $κ$ is consistent. This answers an open question from arXiv:1611.08140 .
