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A tail club guessing ideal can be saturated without being a restriction of the nonstationary ideal. (English) Zbl 1095.03040
Summary: We outline the proof of the consistency that there exists a saturated tail club guessing ideal on \(\omega_1\) which is not a restriction of the nonstationary ideal. A new class of forcing notions and the forcing axiom for the class are introduced for this purpose.

MSC:
03E05 Other combinatorial set theory
03E35 Consistency and independence results
03E55 Large cardinals
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