Two-cardinal versions of weak compactness: partitions of pairs
type: Item
instance of: scholarly article
title: Two-cardinal versions of weak compactness: partitions of pairs
zbMATH Open document ID: 1254.03083
author: Pierre Matet
author: Toshimichi Usuba
published in: Annals of Pure and Applied Logic
publication date: 2011-11-11T00:00:00Z
review text: The authors study various partition properties on \(P_{\kappa}^{\lambda}\). They consider ideals associated with these partition properties, so for instance the ideal \(I_{\kappa,\lambda}\) (the noncofinal ideal), \(\mathrm{NSS}_{\kappa,\lambda}\) (the smallest seminormal ideal), \(\mathrm{NSh}_{\kappa,\lambda}\) (the \(\lambda\)-Shelah ideal). Their main result asserts that if \(\lambda^{<\lambda^{<\kappa}} = \lambda^{<\kappa}\), then \(p(\mathrm{NSh}_{\kappa,\lambda^{<\kappa}}))^+ \rightarrow (\mathrm{NSS}^+_{\kappa,\lambda})^2\), where \(p : P_{\kappa}(\lambda^{<\kappa}) \rightarrow P_{\kappa}(\lambda)\) is defined by \(p(x) = x \cap \lambda\). In their paper they review basic material and study elementary properties of the ideals \(\mathrm{NSJ}_{\kappa,\lambda}\), \(\mathrm{NJ}_{\kappa,\lambda}\), \(\mathrm{NSB}_{\kappa,\lambda}\) and \(\mathrm{NB}_{\kappa,\lambda}\). They investigate very strongly normal ideals and give an overview of the results under GCH.
reviewed by: Martin Weese
Mathematics Subject Classification ID: 03E02
Mathematics Subject Classification ID: 03E55
zbMATH DE Number: 5970593
zbMATH Keywords: weakly compact cardinal
zbMATH Keywords: partition relation
zbMATH Keywords: \(P_{\kappa}^{\lambda}\)
MaRDI profile type: Publication
full work available at URL: j.apal.2011.08.001
OpenAlex ID: W2033248392
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DOI: 10.1016/J.APAL.2011.08.001
description: scientific article; zbMATH DE number 5970593