Cardinal functions on initial chain algebras on pseudotrees
type: Item
instance of: scholarly article
title: Cardinal functions on initial chain algebras on pseudotrees
zbMATH Open document ID: 0965.06014
DOI: 10.1023/A:1006415818082
author: Lynne Baur
published in: Order
publication date: 2001-07-22T00:00:00Z
review text: A pseudotree is a partially ordered set such that the collection of elements below a given element is simply ordered. Taking those collections as generators, one forms a Boolean algebra of subsets of the pseudotree, called the initial chain algebra of it. The author investigates the relationships between the following common cardinal functions in such algebras: depth, tightness, spread, hereditary Lindelöf degree, cellularity, incomparability, hereditary cofinality, cardinality, and irredundance. Several theorems show that some of these functions coincide for initial chain algebras. The results seem to be rather complete. The Stone space of such an algebra is characterized.
Mathematics Subject Classification ID: 06E05
Mathematics Subject Classification ID: 06E10
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 06E15
zbMATH DE Number: 1523422
zbMATH Keywords: initial chain algebra
zbMATH Keywords: pseudotree
zbMATH Keywords: cardinal functions
zbMATH Keywords: depth
zbMATH Keywords: tightness
zbMATH Keywords: hereditary Lindelöf degree
zbMATH Keywords: Boolean algebra
zbMATH Keywords: spread
zbMATH Keywords: cellularity
zbMATH Keywords: hereditary cofinality
zbMATH Keywords: incomparability
zbMATH Keywords: irredundance
zbMATH Keywords: Stone space
reviewed by: J. Donald Monk
MaRDI profile type: Publication
full work available at URL: a:1006415818082
OpenAlex ID: W105260552
description: scientific article; zbMATH DE number 1523422