• Corpus ID: 244773371

Partitioning the real line into Borel sets

  title={Partitioning the real line into Borel sets},
  author={William R. Brian},
  • W. Brian
  • Published 1 December 2021
  • Mathematics
For what infinite cardinals κ is there a partition of the real line R into precisely κ Borel sets? Hausdorff famously proved that there is a partition of R into א1 Borel sets. But other than this, we show that the spectrum of possible sizes of partitions of R into Borel sets can be fairly arbitrary. For example, given any A ⊆ ω with 0, 1 ∈ A, there is a forcing extension in which A = {n : there is a partition of R into אn Borel sets}. We also look at the corresponding question for partitions of… 



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