Splitting positive sets

We introduce a class of cardinal invariants s ℐ for ideals ℐ on ω which arise naturally from the FinBW property introduced by Filipów et al. (2007). Let ℐ be an ideal on ω . Define s I = min { ∣ X ∣ : X ⊂ [ ω ] ω , ∀ B ∈ I + , ∃ x ∈ X ( B ∖ x , B ∩ x ∈ [ ω ] ω ) } . We characterize them and compare...

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Bibliographic Details
Published inScience China. Mathematics Vol. 66; no. 11; pp. 2457 - 2470
Main Authors Zhang, Hang, He, Jialiang, Zhang, Shuguo
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.11.2023
Springer Nature B.V
Subjects
Applications of Mathematics
Invariants
Mathematics
Mathematics and Statistics
40A30
forcing
03E15
03E17
ideal convergence
cardinal invariant
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Summary:We introduce a class of cardinal invariants s ℐ for ideals ℐ on ω which arise naturally from the FinBW property introduced by Filipów et al. (2007). Let ℐ be an ideal on ω . Define s I = min { ∣ X ∣ : X ⊂ [ ω ] ω , ∀ B ∈ I + , ∃ x ∈ X ( B ∖ x , B ∩ x ∈ [ ω ] ω ) } . We characterize them and compare them with other cardinal invariants of the continuum.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-022-2066-x