Journal of Symbolic Logic 63 (4):1437-1441 (1998)

Abstract
It is proved consistent that there be a proper $\sigma$-ideal $\Im$ on $\omega_1$ and an $\aleph_1$-preserving poset $\mathbb{P}$ such that $\mathbb{P} \Vdash$ the $\sigma$-ideal generated by $\check{\Im}$ is not proper
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DOI http://projecteuclid.org/euclid.jsl/1183745641
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