Abstract
We introduce a class of cardinal invariants sℐ 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 sI=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.
| Original language | English |
|---|---|
| Pages (from-to) | 2457-2470 |
| Number of pages | 14 |
| Journal | Science China Mathematics |
| Volume | 66 |
| Issue number | 11 |
| DOIs | |
| State | Published - Nov 2023 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2023, Science China Press.
Funding
This work was supported by National Natural Science Foundation of China (Grant Nos. 11601443, 11801386 and 11771311). The authors are grateful to the referees for careful reading of the manuscript, corrections, and comments which greatly improved this paper. Theorem 4.1 was proved only for the case where λ = ω and κ = ω in an early version of this paper. Both referees encourage us to prove the generalized version. One of the referees kindly provide (3) and (4) of Lemma 4.4. He (or She) also provides Remark 4.11. 1 2
| Funders | Funder number |
|---|---|
| National Natural Science Foundation of China | 11601443, 11771311, 11801386 |
Keywords
- 03E15
- 03E17
- 40A30
- cardinal invariant
- forcing
- ideal convergence