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

##
Hereditarily normality of *gamma**N*

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
`gamma`*N* 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`
`gamma`*N*-space''.

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