# 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}
}
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…
1 Citations

## References

SHOWING 1-7 OF 7 REFERENCES
Combinatorics of dense subsets of the rationals
• Mathematics
• 2004
We study combinatorial properties of the partial order (Dense(Q); ). To do that we introduce cardinal invariants pQ; tQ; hQ; sQ; rQ; iQ describing properties of Dense(Q). These invariants satisfy pQ
Small Combinatorial Cardinal Characteristics and Theorems of Egorov and Blumberg
• Mathematics
• 2000
We will show that the following set theoretical assumption c = ω2, the dominating number d equals to ω1, and there exists an ω1-generated Ramsey ultrafilter on ω (which is consistent with ZFC)
ON I AND I∗-EQUAL CONVERGENCE AND AN EGOROFF-TYPE THEOREM
• Mathematics
• 2013
In this paper we extend the notion of equal convergence of Császár and Laczkovich with the help of ideals of the set of positive integers and introduce the ideas of I and I∗-equal convergence and
Combinatorial Cardinal Characteristics of the Continuum
The combinatorial study of subsets of the set N of natural numbers and of functions from N to N leads to numerous cardinal numbers, uncountable but no larger than the continuum. For example, how many
More on cardinal invariants of analytic P-ideals
• Mathematics
• 2009
Given an ideal $I$ on $\omega$ let $a(I)$ ($\bar{a}(I)$) be minimum of the cardinalities of infinite (uncountable) maximal $I$-almost disjoint subsets of $[{\omega}]^{\omega}$, and denote $b_I$
Analytic Quotients: Theory of Liftings for Quotients over Analytic Ideals on the Integers
Introduction Baire-measurable homomorphisms of analytic quotients Open coloring axiom and uniformization Homomorphisms of analytic quotients under OCA Weak extension principle Gaps and limits in
Cardinal invariants of analytic quotient, Slides for ESI workshop on large cardinals and descriptive set theory, Vienna
• 2009