[FOM] paedogogic question

[Thomas Forster]

Just tidying up my set theory notes before lectures
start next week.  First stop: independence proofs.

The hereditarily countable sets are the usual way of 
demonstrating the independence of power set: they
model everything else after all - and you even get 
AC free beco's everything is countable.  However, for
the hereditarily countable sets to be a mode of sumset
one seems to need choice to hold in the theory one is 
working in.  

Does one just skate over this point on the grounds
that The Masses all believe AC anyway?  Or is there
a cute structure that proves the independence of Power
set without any weasling at all?  (I should know this!)

     Thomas Forster




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