# Sh:811

• Geschke, S., & Shelah, S. (2003). Some notes concerning the homogeneity of Boolean algebras and Boolean spaces. Topology Appl., 133(3), 241–253.
• 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\leq 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,\dots,h_n of B such that 1=h_1(a)\cup\dots\cup h_n(a).
• Version 2003-04-11_11 (11p) published version (13p)
Bib entry
@article{Sh:811,
author = {Geschke, Stefan and Shelah, Saharon},
title = {{Some notes concerning the homogeneity of Boolean algebras and Boolean spaces}},
journal = {Topology Appl.},
fjournal = {Topology and its Applications},
volume = {133},
number = {3},
year = {2003},
pages = {241--253},
issn = {0166-8641},
mrnumber = {2000501},
mrclass = {03G05 (03E05 06E15 54D30 54F05)},
doi = {10.1016/S0166-8641(03)00103-2},
note = {\href{https://arxiv.org/abs/math/0211399}{arXiv: math/0211399}},
arxiv_number = {math/0211399}
}