Cardinal invariants about shrinkability of unbounded sets
type: Item
instance of: scholarly article
title: Cardinal invariants about shrinkability of unbounded sets
zbMATH Open document ID: 0869.03027
DOI: 10.1016/S0166-8641(96)00057-0
author: Masaru Kada
author: Yoshifumi Yuasa
published in: Topology and its Applications
publication date: 1997-08-24T00:00:00Z
review text: The authors study the cardinal number \(\mathfrak b^*\), defined as the minimal cardinal \(\lambda\) with the property that every unbounded family -- in the mod-finite order on \(\omega^\omega\) -- can be shrunk to an unbounded subfamily of size \(\lambda\) or less. This cardinal number was used in the study of the tightness of products of sequential fans. In this paper the definition is extended to cover general ideals of subsets and the resulting invariant is denoted by \(\text{shr}({\mathcal I})\). The main results of the paper give the position of the values of this new invariant for the ideals of meager and null sets in Cichoń's diagram as well as the consistency of various strict inequalities.
reviewed by: K. P. Hart
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 987926
zbMATH Keywords: shrinkability
zbMATH Keywords: ideals
zbMATH Keywords: null sets
zbMATH Keywords: Cichoń's diagram
zbMATH Keywords: strict inequalities
zbMATH Keywords: meager sets
zbMATH Keywords: unbounded family
MaRDI profile type: Publication
cites work: Combinatorial aspects of measure and category
cites work: Q4844091
cites work: The Cichoń diagram
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full work available at URL: s0166-8641(96)00057-0
OpenAlex ID: W2062548831
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description: scientific article; zbMATH DE number 987926