• DOI:10.4064/CM134-2-3
• Corpus ID: 124448794

The reaping and splitting numbers of nice ideals

@article{Filipw2014TheRA,
  title={The reaping and splitting numbers of nice ideals},
  author={Rafal Filip{\'o}w},
  journal={Colloquium Mathematicum},
  year={2014},
  volume={134},
  pages={179-192}
}

• Rafal Filipów
• Published 2014
• Mathematics
• Colloquium Mathematicum

We examine the splitting number s(B) and the reaping number r(B) of quotient Boolean algebras B = P(ω)/I over Fσ ideals and analytic P-ideals. For instance we prove that under Martin’s axiom s(P(ω)/I) = c for all Fσ ideals and analytic P-ideals with BW property (and one cannot drop the assumption about BW property). On the other hand we prove that under Martin’s axiom r(P(ω)/I) = c for all Fσ ideals and analytic P-ideals (in this case we do not need the assumption about BW property). We also provide applications of these characteristics to the ideal convergence of sequences of real-valued functions defined on reals.