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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:
 300000 Other combinatorial set theory 3e+35 Consistency and independence results 3e+55 Large cardinals
##### Keywords:
consistency; saturated tail club guessing ideal; forcing
Full Text:
##### References:
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