Nonsplitting Subset of $mathscr{P}_kappa(kappa^+)$

Journal of Symbolic Logic 50 (4):881-894 (1985)
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Assuming the existence of a supercompact cardinal, we construct a model of ZFC + (There exists a nonsplitting stationary subset of $\mathscr{P}_|kappa(\kappa^+)$). Answering a question of Uri Abraham [A], [A-S], we prove that adding a real to the world always makes $\mathscr{P}_{\aleph_1}(\aleph_2) - V$ stationary



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