[FOM] complete atomless boolean algebras

[A.P. Hazen]

Robert Black asks  two questions about complete atomless Boolean algebras.
I discuss such algebras (briefly!) in a paper, "Hypergunk,"  in  "The 
Monist," vol. 87 (2004), pp. 322-338.
I ***think*** (but am nervously aware that I wasn't terribly rigorous 
in my proofs when I was writing the paper) that the answer to Black's 
questions is "Yes".  One way of getting complete atomless  Boolean 
algebras is to take the algebras of regular open sets from some 
decent topologicalspace.  One way to get a topological space is by 
starting with the reals or some analogue of them.  One  way of 
getting reals is by taking omega-length sequences of objects chosen 
from some finite set (in other words, decimal expansions).  What I 
***think*** gives the answer  is using, as analogues of the real 
numbers, decimal expansions where  the  length of the sequnece is, 
not  omega but, an  inaccessible ordinal.
((If this  is wrong... well,I've made embarrassing mistakes before.))

Allen Hazen
Philosophy Department
University of Melbourne