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 $\mathfrak{b}<2^{{\mathrm{\aleph }}_n}={\mathrm{\aleph }}_{n+1}$, if $\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.0.3/svg/25fb.svg">}({\mathrm{\aleph }}_{n+1})$ holds, then there exists an ${\mathrm{\aleph }}_{n+1}$-Souslin tree.

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Citation information:

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