[FOM] complete atomless boolean algebras

[Robert Black]

I have two questions about complete atomless boolean algebras to 
which I find I can't (or can't easily) get answers from the 
Koppelberg Handbook, but I expect there are members of this list who 
can answer them instantly:

1) An infinite complete boolean algebra must have a cardinality k 
such that k=k^aleph_0. Is this the only cardinality restriction on 
complete *atomless* Boolean algebras? In particular, can the 
cardinality of a complete atomless Boolean algebra be inaccessible?

2) A Boolean algebra B is homogeneous (I think this is the standard 
word) iff for every nonzero p in B, the algebra induced on the x in B 
less than or equal to p by the partial order inherited from B is 
isomorphic to the whole of B. Trivially a homogeneous Boolean algebra 
with cardinality greater than 2 is atomless. Now consider *complete* 
homogeneous Boolean algebras. (There are such things, since unless 
I'm making an embarrassing mistake the regular open algebra over R is 
one.) Same question again: what cardinalities can complete 
homogeneous Boolean algebras have, and in particular can their 
cardinality be inaccessible?

Robert