2018/01/29 by Raghavan, Dilip, Shelah, Saharon · 1 citation
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1801.09369
We prove two ZFC theorems about cardinal invariants above the continuum which are in sharp contrast to well-known facts about these same invariants at the continuum. It is shown that for an uncountable regular cardinal κ, \mathfrakb(κ) = κ+ implies \mathfraka(κ) = κ+. This improves an earlier result of Blass, Hyttinen, and Zhang. It is also shown that if κ≥ \bethω is an uncountable regular cardinal, then \mathfrakd(κ) ≤ \mathfrakr(κ). This result partially dualizes an earlier theorem of the authors.