On the ideal $J[κ]$

英文摘要：

Motivated by a question from a recent paper by Gilton, Levine and Stejskalova, we obtain a new characterization of the ideal $J[κ]$, from which we confirm that $κ$-Souslin trees exist in various models of interest. As a corollary we get that for every integer $n$ such that $\mathfrak b<2^{\aleph_n}=\aleph_{n+1}$, if $\square(\aleph_{n+1})$ holds, then there exists an $\aleph_{n+1}$-Souslin tree.