2022/02/01 by Alan Dow, Saharon Shelah, Dow, Alan +1
Computer Science · Mathematics · #03E15 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2202.00372
openalex publication_date 2022/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The cardinal invariants \mathfrak h, \mathfrak b, \mathfrak s of \mathcal P (ω) are known to satisfy that ω1 ≤ \mathfrak h ≤min\\mathfrak b, \mathfrak s\. We prove that all inequalities can be strict. We also introduce a new upper bound for \mathfrak h and show that it can be less than \mathfrak s. The key method is to utilize finite support matrix iterations of ccc posets following \citeBlassShelah.