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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.

03E05 Other combinatorial set theory
03E35 Consistency and independence results
03E55 Large cardinals
Full Text: DOI
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