Towers in \([\omega]^{\omega}\) and \(^{\omega}\omega\) (Q1262305)
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scientific article; zbMATH DE number 4123716
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Towers in \([\omega]^{\omega}\) and \(^{\omega}\omega\) |
scientific article; zbMATH DE number 4123716 |
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Towers in \([\omega]^{\omega}\) and \(^{\omega}\omega\) (English)
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1989
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The author studies the sets \(A=\{\kappa |\) there is a \(\kappa\)-tower in \([\omega]^{\omega}\}\) and \(B=\{\kappa |\) there is a \(\kappa\)- tower in \(^{\omega}\omega \}\), and shows that in ZFC either \(B\subseteq A\) or else there is a scale in \(^{\omega}\omega\). The bulk of the paper consists of forcing extensions in which A (and possibly B, too) can be certain preassigned sets and various relationships hold between cardinals associated with the respective partial orderings.
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cardinals associated with partial orderings
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\(\kappa\)-tower
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scale
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forcing extensions
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