# Sh:599

- Rosłanowski, A., & Shelah, S. (2000).
*More on cardinal invariants of Boolean algebras*. Ann. Pure Appl. Logic,**103**(1-3), 1–37. arXiv: math/9808056 DOI: 10.1016/S0168-0072(98)00066-9 MR: 1756140 -
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}, mrnumber = {1756140}, mrclass = {03G05 (03E05 03E35 06E05)}, doi = {10.1016/S0168-0072(98)00066-9}, note = {\href{https://arxiv.org/abs/math/9808056}{arXiv: math/9808056}}, arxiv_number = {math/9808056} }