The almost disjointness cardinal invariant in the quotient algebra of the rationals modulo the nowhere dense subsets.
type: Item
instance of: scholarly article
title: The almost disjointness cardinal invariant in the quotient algebra of the rationals modulo the nowhere dense subsets.
zbMATH Open document ID: 1052.03027
author: Juris Steprāns
published in: Real Analysis Exchange
publication date: 2004-08-06T00:00:00Z
review text: Let \(B\) be a Boolean algebra that does not have the countable chain condition. Then \({\mathfrak a}(B)\) denotes the least uncountable cardinal of an uncountable maximal antichain. This generalizes the almost disjointness number of the continuum. Let \(\mathcal N\) be the ideal of nowhere dense subsets of \(\mathbb{Q}\). Then \({\mathfrak a}{{\mathcal N}}\) denotes \({\mathfrak a}({\mathcal P}(\mathbb{Q})/{\mathcal N})\). The author shows that in the iterated Laver model \({\mathfrak a} =\aleph_2\) but \({\mathfrak a}({\mathcal N}) =\aleph_1\). Further on he shows that \({\mathfrak a}({\mathcal N})\geq {\mathfrak p}\), thus \({\mathfrak a}({\mathcal N})\) can be arbitrarily large.
reviewed by: Martin Weese
Mathematics Subject Classification ID: 03E17
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 2084013
zbMATH Keywords: almost disjointness number
zbMATH Keywords: nowhere dense set
zbMATH Keywords: Laver forcing
MaRDI profile type: Publication
full work available at URL: realanalexch.27.2.0795
OpenAlex ID: W2157221406
DOI: 10.14321/REALANALEXCH.27.2.0795
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description: scientific article; zbMATH DE number 2084013