Sh:620
- Shelah, S. (1999). Special subsets of ^{\mathrm{cf}(\mu)}\mu, Boolean algebras and Maharam measure algebras. Topology Appl., 99(2-3), 135–235. arXiv: math/9804156 DOI: 10.1016/S0166-8641(99)00138-8 MR: 1728851
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Abstract:
The original theme of the paper is the existence proof of “there is a (\lambda,J)-sequence for a sequence of ideals \bar{I} = \langle I_i : i < \delta\rangle." This can be thought of as a generalization to Luzin sets and to Sierpinski sets, but for the product \prod\limits_{i < \delta} dom(I_i), the existence proofs are related to pcf.The second theme is when does a Boolean algebra \mathbf{B} have a free caliber \lambda (i.e. if X\subseteq \mathbf{B} and |X| = \lambda, then there exists an independent subset of X of cardinality \lambda). We consider the question when \mathbf{B} is a Maharam measure algebra, or a (small) product of free Boolean algebras, and for \kappa-cc Boolean algebras. A central case is \lambda = (\beth_\omega)^+, or more generally \lambda= \mu^+ for \mu strong limit singular of “small" cofinality. The second case is \mu = \mu^{< \kappa} < \lambda < 2^\mu; we mainly consider \lambda regular, but we also have things to say on the singular case. Lastly, we deal with ultraproducts of Boolean algebras in relation to irr(-) and s(-), etc.
- Version 2015-06-02_10 (143p) published version (101p)
Bib entry
@article{Sh:620,
author = {Shelah, Saharon},
title = {{Special subsets of $^{\mathrm{cf}(\mu)}\mu$, Boolean algebras and Maharam measure algebras}},
journal = {Topology Appl.},
fjournal = {Topology and its Applications},
volume = {99},
number = {2-3},
year = {1999},
pages = {135--235},
issn = {0166-8641},
mrnumber = {1728851},
mrclass = {03E05 (03E04 03E35 03E75 06E05 28A60)},
doi = {10.1016/S0166-8641(99)00138-8},
note = {\href{https://arxiv.org/abs/math/9804156}{arXiv: math/9804156}},
arxiv_number = {math/9804156},
conference = {8th Prague Topological Symposium on General Topology and its Relations to Modern Analysis and Algebra, Part II (1996)}
}