[FOM] The Width of V

[Alasdair Urquhart]

There's an old article by Gaisi Takeuti,
called "Hypotheses on Power Set", published
in the AMS Axiomatic Set Theory volume
(Proceedings of Symposia in Pure Mathematics,
Volume XIII, part 1, 1971).  He gives various 
hypotheses, each of which is intended to say
that the power set of an infinite set is
very rich.

However, my knowledge of set theory ends around
1971.  Does any knowledgeable set theorist know
if there was follow-up to Takeuti's work?