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Feb 11, 2012 at 18:58 comment added Stefan Hoffelner Thank you again! Actually this approach was my first idea of how to prove the claims but I falsely thought that the Boolean algebra $B_\eta$ is isomorphic to the product of the $(B_\xi)_{\xi < \eta}$ (which is as I belive only true for inverse limits?). After realizing my error I didn't continue to think in that direction as I couldn't figure out how the embeddings $B_{\xi} \rightarrow B_{\eta}$ actually look like. But anyway thank you a lot!
Feb 11, 2012 at 18:02 history answered Andreas Blass CC BY-SA 3.0