>Date: Sat, 17 Jul 1999 14:59:54 +0100 >From: Robert Black <Robert.Black at nottingham.ac.uk> >(1) Am I right to guess that the claim is not provable in ZFC? For the claim to be false it suffices that for any k there is >k (say k^+) different cardinals between k and 2^k, which seems to be easily achievable by forcing. V.Kanovei