The reaping and splitting numbers of nice ideals

Rafał Filipów

Colloquium Mathematicae (2014)

  • Volume: 134, Issue: 2, page 179-192
  • ISSN: 0010-1354

Abstract

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We examine the splitting number (B) and the reaping number (B) of quotient Boolean algebras B = (ω)/ℐ where ℐ is an F σ ideal or an analytic P-ideal. For instance we prove that under Martin’s Axiom ((ω)/ℐ) = for all F σ 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 F σ 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.

How to cite

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Rafał Filipów. "The reaping and splitting numbers of nice ideals." Colloquium Mathematicae 134.2 (2014): 179-192. <http://eudml.org/doc/283501>.

@article{RafałFilipów2014,
abstract = {We examine the splitting number (B) and the reaping number (B) of quotient Boolean algebras B = (ω)/ℐ where ℐ is an $F_\{σ\}$ ideal or an analytic P-ideal. For instance we prove that under Martin’s Axiom ((ω)/ℐ) = for all $F_\{σ\}$ 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 $F_\{σ\}$ 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.},
author = {Rafał Filipów},
journal = {Colloquium Mathematicae},
keywords = {Boolean algebra; quotient Boolean algebra; cardinal characteristic; cardinal invariant; analytic P-ideal; ideal convergence; filter convergence; Bolzano-Weierstrass property; splitting number; reaping number; Martin's axiom},
language = {eng},
number = {2},
pages = {179-192},
title = {The reaping and splitting numbers of nice ideals},
url = {http://eudml.org/doc/283501},
volume = {134},
year = {2014},
}

TY - JOUR
AU - Rafał Filipów
TI - The reaping and splitting numbers of nice ideals
JO - Colloquium Mathematicae
PY - 2014
VL - 134
IS - 2
SP - 179
EP - 192
AB - We examine the splitting number (B) and the reaping number (B) of quotient Boolean algebras B = (ω)/ℐ where ℐ is an $F_{σ}$ ideal or an analytic P-ideal. For instance we prove that under Martin’s Axiom ((ω)/ℐ) = for all $F_{σ}$ 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 $F_{σ}$ 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.
LA - eng
KW - Boolean algebra; quotient Boolean algebra; cardinal characteristic; cardinal invariant; analytic P-ideal; ideal convergence; filter convergence; Bolzano-Weierstrass property; splitting number; reaping number; Martin's axiom
UR - http://eudml.org/doc/283501
ER -

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