# Sh:811

- Geschke, S., & Shelah, S. (2003).
*Some notes concerning the homogeneity of Boolean algebras and Boolean spaces*. Topology Appl.,**133**(3), 241–253. arXiv: math/0211399 DOI: 10.1016/S0166-8641(03)00103-2 MR: 2000501 -
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). - 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}, doi = {10.1016/S0166-8641(03)00103-2}, mrclass = {03G05 (03E05 06E15 54D30 54F05)}, mrnumber = {2000501}, mrreviewer = {Judith Roitman}, doi = {10.1016/S0166-8641(03)00103-2}, note = {\href{https://arxiv.org/abs/math/0211399}{arXiv: math/0211399}}, arxiv_number = {math/0211399} }