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Friday, November 18, 2005

**Abstract:** Farah and Solecki asked if every uncountable Polish group contains Polishable subgroups of arbitrarily high Borel rank. Hjorth gave a positive answer for abelian groups and went on to make the following conjecture: There is an uncountable Polish group all of whose abelian subgroups are discrete. I will state a theorem that proves Hjorth's conjecture and sketch its proof. On the other hand, we show that the Farah-Solecki question could be approached otherwise.