On the ideal $J[\kappa]$

Motivated by a question from a recent paper by Gilton, Levine and Stejskalová, 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 b < 2n = אn+1, if (אn+1) holds, then there exists an אn+1-Souslin tree.

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