A. P. Nyikos, L. Soukup and B. Velickovic:

Hereditarily normality of gammaN

We show that ander PFA every countably compact T_5 space is sequentially compact; moreover every countable subset of a countably compact T_5 space has compact, Fréchet-Urysohn closure. The key is the proof is the following result: if PFA holds then no gammaN can be T_5.
On the other hand, we also show that Martin's Axiom is not enough: Let kappa >omega_1 be a cardinal such that kappa^{<kappa}=kappa. Then there is a ccc forcing notion P such that V^P satisfies MA +2^omega=kappa + ``there is a T_5 gammaN-space''.

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    appeared in Topology and its Applications, 65 (1995), pp. 9--19.