Electronic Version 23 Spring (1998)

Mirna Dzamonja

We investigate a question of Y. Benyamini, M. E. Rudin and M. Wage, on the existence of universal uniform Eberlein compacta of a given weight, more exactly the related question of the existence of a universal c-algebra of a given size. We show that for any regular \lambda > \aleph₁ with 2^\aleph₀ > \lambda, there is no c-algebra of size \lambda universal under c-embeddings. In fact, under these circumstances, for no \mu < 2^\aleph₀ are there \mu c-algebras of size \lambda such that every c-algebra of size \lambda c-embeds into one of the \mu given ones.

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topology proceedings Electronic Version