Towers in \([\omega]^{\omega}\) and \(^{\omega}\omega\)
type: Item
instance of: scholarly article
title: Towers in \([\omega]^{\omega}\) and \(^{\omega}\omega\)
zbMATH Open document ID: 0686.03024
DOI: 10.1016/0168-0072(89)90038-9
author: Peter Lars Dordal
published in: Annals of Pure and Applied Logic
publication date: 1989-01-01T00:00:00Z
review text: 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.
reviewed by: K.Gloede
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 4123716
zbMATH Keywords: cardinals associated with partial orderings
zbMATH Keywords: \(\kappa\)-tower
zbMATH Keywords: scale
zbMATH Keywords: forcing extensions
MaRDI profile type: Publication
full work available at URL: 0168-0072(89)90038-9
OpenAlex ID: W2021991928
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description: scientific article; zbMATH DE number 4123716