We examine the splitting number (B) and the reaping number (B) of quotient Boolean algebras B = (ω)/ℐ where ℐ is an ideal or an analytic P-ideal. For instance we prove that under Martin’s Axiom ((ω)/ℐ) = for all ideals ℐ and for all analytic P-ideals ℐ with the BW property (and one cannot drop the BW assumption). On the other hand under Martin’s Axiom ((ω)/ℐ) = for all ideals and all analytic P-ideals ℐ (in this case we do not need the BW property). We also provide applications of these characteristics to the ideal convergence of sequences of real-valued functions defined on the reals.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-3,
author = {Rafa\l\ Filip\'ow},
title = {The reaping and splitting numbers of nice ideals},
journal = {Colloquium Mathematicae},
volume = {135},
year = {2014},
pages = {179-192},
zbl = {1337.03075},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-3}
}
Rafał Filipów. The reaping and splitting numbers of nice ideals. Colloquium Mathematicae, Tome 135 (2014) pp. 179-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-3/