Let $ \lambda\geq \omega_2$ be a regular cardinal and $ S\subset[\lambda]^\omega$ be a stationary set. I’m looking for a property of $ S$ , say “shootable”, such that there exists a forcing extension preserving $ \lambda, \omega_1$ as cardinals that shoots a club into $ S$ . I’ve encountered ad hoc examples, but I’d really hope if there are more explicit descriptions of a stationary set being “shootable” and given that a canonically defined reasonable forcing to shoot a club through it. I’m flexible with any cardinal arithmetic assumptions.
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