More homogeneous almost disjoint families.
type: Item
instance of: scholarly article
title: More homogeneous almost disjoint families.
zbMATH Open document ID: 1063.54030
author: Judith Roitman
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: S. Shelah and J. Steprans showed the consistency of the existence of an uncountable almost disjoint family \(\mathcal A\) on \(\omega \) which generates a Boolean algebra \(A\) (i.e.\ if \(B\) is an uncountable subalgebra of \(A\) and \(\forall n \in \omega \) it holds \(\{ n \} \in B\) then \(A\) is isomorphic to \(B\)). The author proves a generalization of the previous result. The following is consistent: there exists an uncountable almost disjoint family \(\mathcal A\) on \(\omega \) which generates a Boolean algebra isomorphic to every uncountable (weak) subalgebra.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 54G20
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 06E99
zbMATH DE Number: 2158780
zbMATH Keywords: Boolean algebra
zbMATH Keywords: homogeneous Boolean algebra
zbMATH Keywords: almost disjoint family
MaRDI profile type: Publication
full work available at URL: s00012-002-8189-9
OpenAlex ID: W1995164211
DOI: 10.1007/S00012-002-8189-9
description: scientific article; zbMATH DE number 2158780