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Some recent results on Cohen algebras. (English) Zbl 0968.03059

The Cohen algebra \({\mathcal C}_X\) is the Boolean algebra of regular open subsets of the generalized Cantor space \(\{0,1\}^X\). A category algebra is the direct sum of countably many Cohen algebras.
This paper deals with the question whether a complete subalgebra of a category algebra is a category algebra. This can be reduced to the question whether a complete subalgebra of a Cohen algebra is a category algebra. It was shown by Koppelberg that this is true if \(|X|\leq\omega_1\), Later on it was shown by Koppelberg and Shelah that there exists (in ZFC) a subalgebra of \({\mathcal C}_{\omega_2}\) which is not a category algebra. Here the author gives a simplified presentation of the last result.

MSC:

03E40 Other aspects of forcing and Boolean-valued models
06E05 Structure theory of Boolean algebras
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