In [1] Fedorcuk, using diamond, proved that there is a hereditarily separable compact space of cardinality $2^{2^\omega}$.To my best knowledge, Kunen created a humanly digestible proof, but he has not published it (and he passed away). Can I find Kunen's proof somewhere? Or do you know any other proof of the theorem of Fedorcuk?

[1] Fedorčuk, V. V. The cardinality of hereditarily separable bicompacta. (Russian) Dokl. Akad. Nauk SSSR 222 (1975), no. 2, 302–305.


1 Answer 1


I was informed that the following joint paper of Dzamoja and Kunen contains the proof I was looking for.

Dz̆amonja, Mirna; Kunen, Kenneth Measures on compact HS spaces. Fund. Math. 143 (1993), no. 1, 41–54.

  • $\begingroup$ Istvan presented Kunen's proof during a course in Amsterdam around 1980; he had a photocopy at the time. $\endgroup$
    – KP Hart
    Feb 21, 2023 at 7:08
  • $\begingroup$ @KP Hart. He had. But he could not find it. Anyway, we think that we could recover the original argument from the Dzamonja-Kunen paper. $\endgroup$ Feb 22, 2023 at 17:12

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