The consistency of \(``\neg CH+pa\leq \omega_ 1''\) (Q750434)
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scientific article; zbMATH DE number 4174918
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The consistency of \(``\neg CH+pa\leq \omega_ 1''\) |
scientific article; zbMATH DE number 4174918 |
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The consistency of \(``\neg CH+pa\leq \omega_ 1''\) (English)
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1990
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For any cardinal \(\kappa\) of uncountable cofinality the author constructs a model of ZFC in which \(2^{\aleph_ 0}=\kappa\) and the pseudoaltitude pa(A) of every infinite Boolean algebra A is not greater than \(\aleph_ 1\). The pseudoaltitude pa(A) is the minimal cardinal \(\alpha\) such that some ultrafilter in some homomorphic image of A is \(\alpha\)-generated but not \(<\alpha\)-generated. The result strengthens related result by \textit{W. Just} [Algebra Univers. 25, 283-289 (1988; Zbl 0656.06014)] for the altitude of Boolean algebras.
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Continuum Hypothesis
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pseudoaltitude
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infinite Boolean algebra
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