Lusin sequences under CH and under Martin's Axiom
Volume 169 / 2001
Fundamenta Mathematicae 169 (2001), 97-103
MSC: 03E05, 03E50, 03E35.
DOI: 10.4064/fm169-2-1
Abstract
Assuming the continuum hypothesis there is an inseparable sequence of length $\omega _1$ that contains no Lusin subsequence, while if Martin's Axiom and $\neg \rm CH$ are assumed then every inseparable sequence (of length $\omega _1$) is a union of countably many Lusin subsequences.
