Some notes concerning the homogeneity of Boolean algebras and Boolean spaces
Abstract
We consider homogeneity properties of Boolean algebras that have nonprincipal ultrafilters which are countably generated.It is shown that a Boolean algebra B is homogeneous if it is the union of countably generated nonprincipal ultrafilters and has a dense subset D such that for every a in D the relative algebra B restriction a:= {b in B:b <= a} is isomorphic to B. In particular, the free product of countably many copies of an atomic Boolean algebra is homogeneous. Moreover, a Boolean algebra B is homogeneous if it satisfies the following conditions: (i) B has a countably generated ultrafilter, (ii) B is not c.c.c., and (iii) for every a in B setminus {0} there are finitely many automorphisms h_1, ...,h_n of B such that 1=h_1(a) cup ... cup h_n(a).
Cite
@article{arxiv.math/0211399,
title = {Some notes concerning the homogeneity of Boolean algebras and Boolean spaces},
author = {Stefan Geschke and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0211399},
year = {2007}
}