Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

A notion of forcing $P$ is called stationary set preserving iff each stationary subset of $\omega_1$ remains stationary in $V^P$. It is standard to show that semiproper (and of course proper) notions of forcing are stationary set preserving. On the other hand Shelah realized that assuming the Semiproper Forcing Axiom (which is consistent relative to a supercompact cardinal) each stationary set preserving notion is already semiproper. So the question naturally arises if there is a nice example of a notion of forcing which is stationary set preserving but not semiproper?

share|improve this question

1 Answer 1

up vote 6 down vote accepted

Namba forcing is stationary preserving but not semiproper unless Chang's Conjecture holds. See "Proper and Improper Forcing" of Shelah, Ch 12.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.