On the ideal J[kappa]

Abstract. Motivated by a question from a recent paper by Gilton, Levine and Stejskalova, we obtain a new characterization of the ideal $J[\kappa]$, from which we confirm that $\kappa$-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.

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Citation information:

A. Rinot, On the ideal $J[\kappa]$, Ann. Pure Appl. Logic, 172(5): 103055, 13pp, 2022.