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The weakening of the non-existence assumption for $(\clubsuit)$
Weakening conjecture. The assertion $(\clubsuit)$ still holds under much weaker assumptions than the non-existence of $0^\P$ .
Conjectureopeninner-model-theory sharp-operatorsarXiv posted 2 days ago

The weakening of the non-existence assumption for (♣)(\clubsuit)(♣)