Published online by Cambridge University Press: 12 March 2014
In Baire space we define a sequence of equivalence relations ‹Ev ∣ v < , each Ev being with classes in + v + 1 and such that (i) Ev does not have perfectly many classes, and (ii) is countable iff < ω1. This construction can be extended cofinally in . A new proof is given of a theorem of Hausdorff on partitions of R into ω1 many sets.
The main results of this paper were presented at the Sixth International Congress of Logic, Methodology and the Philosophy of Science (Hannover, 1979).