Totally proper forcing and the Moore–Mrówka problem
Volume 177 / 2003
Fundamenta Mathematicae 177 (2003), 121-137
MSC: Primary 03E75.
DOI: 10.4064/fm177-2-2
Abstract
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 ${\rm ZFC}+{\rm CH}$ 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.
