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Garti, Shimon; Shelah, Saharon

(\(\kappa ,\theta \))-weak normality. (English) Zbl 1269.03046

J. Math. Soc. Japan 64, No. 2, 549-559 (2012).
An ultrafilter \(D\) on a cardinal \(\kappa\) is weakly normal if for every regressive function \(f\) on \(\kappa\) there is some \(\alpha_* < \kappa\) such that \(\{ i<\kappa : f(i) \leq \alpha_* \} \in D\).
The authors deal with the notion of weak normality. Let \(\bar{\lambda} = \langle \lambda_i: i<\kappa \rangle\) be a sequence of cardinals with limit \(\lambda\). They characterize the situation of \(|\prod_{i<\kappa} \lambda_i/D| = \lambda\). Further on, they find a necessary condition for a positive answer to a question of Monk on the depth of Boolean algebras.
Reviewer: Martin Weese (Potsdam)

MSC:

03E04 Ordered sets and their cofinalities; pcf theory
03E05 Other combinatorial set theory
06E05 Structure theory of Boolean algebras

Keywords:

ultrafilters; weak normality, Boolean algebras; depth; measurable cardinal
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\textit{S. Garti} and \textit{S. Shelah}, J. Math. Soc. Japan 64, No. 2, 549--559 (2012; Zbl 1269.03046)
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