The reaping and splitting numbers of nice ideals

• Autorzy: Rafał Filipów
• Języki publikacji: EN

Abstrakty

EN

We examine the splitting number 𝔰(B) and the reaping number 𝔯(B) of quotient Boolean algebras B = 𝓟(ω)/ℐ where ℐ is an $F_{σ}$ ideal or an analytic P-ideal. For instance we prove that under Martin's Axiom 𝔰(𝓟(ω)/ℐ) = 𝔠 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 𝔯(𝓟(ω)/ℐ) = 𝔠 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.

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 03E17: Cardinal characteristics of the continuum
• 40A30: Convergence and divergence of series and sequences of functions
• 03E75: Applications of set theory
• 40A35: Ideal and statistical convergence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 134
• Numer: 2
• Strony: 179-192

Daty

wydano

2014

Twórcy

autor

Rafał Filipów

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/cm134-2-3