S-spaces and large continuum (Q6044439)

An S-space is a regular hereditarily separable space that is not Lindelöf. The continuum hypothesis (\(\mathfrak c=\aleph_1\)) implies that there are S-spaces, and the existence of S-spaces is consistent with any value of \(\mathfrak c\). On the other hand, it is consistent with \(\mathfrak c=\aleph_2\) that there are no S-spaces. In the paper under review, the authors prove that it is consistent with any value of \(\mathfrak c>\aleph_2\) that there are no S-spaces. Using a similar method, the authors prove that it is consistent with \(\mathfrak c>\aleph_2\) that every separable Moore-Mrowka space has cardinality at most \(\mathfrak c\).