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.