We describe a totally proper notion of forcing that can be used to shoot uncountable free sequences through certain countably compact non-compact spaces. This is almost (but not quite!) enough to produce a model of ZFC + CH in which countably tight compact spaces are sequential-we still do not know if the notion of forcing described in the paper can be iterated without adding reals.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-2-2,
author = {Todd Eisworth},
title = {Totally proper forcing and the Moore-Mr\'owka problem},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {121-137},
zbl = {1020.03045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-2-2}
}
Todd Eisworth. Totally proper forcing and the Moore-Mrówka problem. Fundamenta Mathematicae, Tome 177 (2003) pp. 121-137. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-2-2/