CH and first countable, countably compact spaces (Q1841979)

This interesting paper is a follow-up and improvement of an earlier paper of the author and \textit{J. Roitman} [Trans. Am. Math. Soc. 351, No. 7, 2675-2693 (1999; Zbl 0921.54004)]. The main result of the paper is to establish the consistency with CH that first countable countably compact spaces are compact if they do not contain an uncountable free sequence. Free sequences arose in the study of countable tightness and a compact space has countable tightness exactly when it has no uncountable free sequences. The main technique is to establish that for a given potential counterexample, there is a poset which forces there to be a free sequence. The challenge is to show that the poset satisfies the iterable condition of being 2-complete, an innovation in the above mentioned paper. It is similar to, and improves upon, the \({\mathbb D}\)-completeness condition from Shelah's proper forcing book.