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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 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.
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 -