Partitioning the real line into Borel sets
Partitioning the real line into Borel sets
For which infinite cardinals $\kappa$ is there a partition of the real line $\mathbb R$ into precisely $\kappa$ Borel sets? Hausdorff famously proved that there is a partition of $\mathbb R$ into $\aleph_1$ Borel sets. But other than this, we show that the spectrum of possible sizes of partitions of …