MA(\(\sigma\)-centered): Cohen reals, strong measure zero sets and strongly meager sets
type: Item
instance of: scholarly article
title: MA(\(\sigma\)-centered): Cohen reals, strong measure zero sets and strongly meager sets
zbMATH Open document ID: 0693.03032
DOI: 10.1007/BF02764965
author: Haim Judah
author: S. Shelah
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: A set \(X\subset {\mathbb{R}}\) is strongly meager if for every Lebesgue measure zero set M there is \(x\in {\mathbb{R}}\) such that \((X+x)\cap M=\emptyset\). The dual Borel conjecture says that every strongly meager set is countable. It was shown by Carlsson that consistency of ZF implies consistency of ZFC \(+\) Dual Borel Conjecture. Here it is shown that consistency of ZF implies also consistency of ZFC \(+\) Dual Borel Conjecture \(+\) MA(\(\sigma\)-centered).
reviewed by: Martin Weese
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E50
zbMATH DE Number: 4134032
zbMATH Keywords: strongly measure zero set
zbMATH Keywords: Cohen real
zbMATH Keywords: strongly meager set
zbMATH Keywords: Dual Borel Conjecture
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4134032