We outline the proof of the consistency that there exists a saturated tail club guessing ideal on ω₁ 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.
"A Tail Club Guessing Ideal Can Be Saturated without Being a Restriction of the Nonstationary Ideal." Notre Dame J. Formal Logic 46 (3) 327 - 333, 2005. https://doi.org/10.1305/ndjfl/1125409331