# Sh:599

• Rosłanowski, A., & Shelah, S. (2000). More on cardinal invariants of Boolean algebras. Ann. Pure Appl. Logic, 103(1-3), 1–37.
• Abstract:
We address several questions of Donald Monk related to irredundance and spread of Boolean algebras, gaining both some ZFC knowledge and consistency results. We show in ZFC that irr(B_0\times B_1)=\max\{irr(B_0),irr(B_1)\}. We prove consistency of the statement “there is a Boolean algebra B such that irr(B)< s(B\otimes B)” and we force a superatomic Boolean algebra B_* such that s(B_*)=inc(B_*)=\kappa, irr(B_*)=Id(B_*)=\kappa^+ and Sub(B_*)=2^{\kappa^+}. Next we force a superatomic algebra B_0 such that irr(B_0)< inc(B_0) and a superatomic algebra B_1 such that t(B_1)> {\rm Aut}(B_1). Finally we show that consistently there is a Boolean algebra B of size \lambda such that there is no free sequence in B of length \lambda, there is an ultrafilter of tightness \lambda (so t(B)=\lambda) and \lambda\notin{\rm Depth}_{\rm Hs}(B).
• published version (37p)
Bib entry
@article{Sh:599,
author = {Ros{\l}anowski, Andrzej and Shelah, Saharon},
title = {{More on cardinal invariants of Boolean algebras}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {103},
number = {1-3},
year = {2000},
pages = {1--37},
issn = {0168-0072},
doi = {10.1016/S0168-0072(98)00066-9},
mrclass = {03G05 (03E05 03E35 06E05)},
mrnumber = {1756140},
mrreviewer = {D. Monk},
doi = {10.1016/S0168-0072(98)00066-9},
note = {\href{https://arxiv.org/abs/math/9808056}{arXiv: math/9808056}},
arxiv_number = {math/9808056}
}