### Two results on cardinal invariants at uncountable cardinals

by Raghavan and Shelah. [RaSh:1135]

Proc Asian Logic Conferences (ALC2015), 2019

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
uncoutable regular cardinal kappa, {b}(kappa) = kappa^+
implies {a}(kappa) = kappa^+ . This improves an earlier
result of Blass, Hyttinen and Zhang [3]. It is also shown that if
kappa >= beta_omega is an uncountable regular cardinal, then
{d} (kappa) <= {r}(kappa) . This result
partially dualizes an earlier theorem of the authors [6]

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