The weight of a countably compact group whose cardinality has countable cofinality
The author obtains a forcing model in which there exists an ultrafilter \(p\) and a \(p\)-compact group whose weight is strictly greater than the cardinality of the group. The cardinality of this group has countable cofinality. As a result, he shows that it is consistent that one can induce on each Boolean group of cardinality \(\lambda \in [c, 2^c]\) a \(p\)-compact group topology of weight strictly larger than \(\lambda\). In the constructed model, CH holds. The work is done in response to the question posed by \textit{E. K. van Douwen} [Proc. Am. Math. Soc. 80, 678--682 (1980; Zbl 0446.54011)], who showed that under GCH any pseudocompact Tychonoff space whose cardinality has countable cofinality, must have cardinality equal to its weight.
scientific article; zbMATH DE number 2173264