Partitioning products of \({\mathcal P} (\omega)/\text{fin}\)
type: Item
instance of: scholarly article
title: Partitioning products of \({\mathcal P} (\omega)/\text{fin}\)
zbMATH Open document ID: 0865.04004
published in: Pacific Journal of Mathematics
publication date: 1996-12-15T00:00:00Z
review text: We generalize the cardinal invariant \({\mathfrak a}\) to products of \({\mathcal P} (\omega)/\text{fin}\) and then sharpen the well-known inequality \({\mathfrak b} \leq {\mathfrak a}\) by proving \({\mathfrak b} \leq {\mathfrak a} (\lambda)\) for every \(\lambda \leq \omega\). Here \({\mathfrak a} (n)\), for \(n< \omega\), is the least size of an infinite partition of \(({\mathcal P} (\omega)/\text{fin})^n\), \({\mathfrak a} (\omega)\) is the least size of an uncountable partition of \(({\mathcal P} (\omega)/ \text{fin})^\omega\), and \({\mathfrak b}\) is the least size of an unbounded family of functions from \(\omega\) to \(\omega\) ordered by eventual dominance. We also prove the consistency of \({\mathfrak b}< {\mathfrak a} (n)\) for every \(n< \omega\).
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 06E05
zbMATH DE Number: 950228
zbMATH Keywords: Boolean algebra
zbMATH Keywords: forcing
zbMATH Keywords: cardinal invariant
zbMATH Keywords: partition
author: Otmar Spinas
reviewed by: Otmar Spinas
MaRDI profile type: Publication
full work available at URL: pjm.1996.176.249
OpenAlex ID: W1574847331
DOI: 10.2140/PJM.1996.176.249
description: scientific article; zbMATH DE number 950228