[FOM] A new definition of Cardinality

[T.Forster@dpmms.cam.ac.uk]

I looked at this a while ago. My recollection is that Jech's technique for 
showing that HC (the hereditarily countable sets) is a set - and of rank 
omega_2 at most - will generalise to show that H_kappa (the sets 
hereditarily of size less than kappa) is a set (and without any use of AC) 
works *as long as kappa is an aleph*. I'll have another look to see if the 
starred condition is needed. It probably is.

 Jech's construction is very elegant.  A nice paper