MA(\(\sigma\)-centered): Cohen reals, strong measure zero sets and strongly meager sets
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).
scientific article; zbMATH DE number 4134032
scientific article