Geodesic
On the existence of a $\sigma $-closed dense subset
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 3, pp. 513-517.

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It is consistent with the axioms of set theory that there are two co-dense partial orders, one of them $\sigma $-closed and the other one without a $\sigma $-closed dense subset.
Classification : 03E40
Keywords: forcing; sigma-closed dense subset 
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Zapletal, Jindřich. On the existence of a $\sigma $-closed dense subset. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 3, pp. 513-517. http://geodesic.mathdoc.fr/item/CMUC_2010__51_3_a12/