Lusin sequences under CH and under Martin's Axiom
Uri Abraham, Saharon Shelah (2001)
Fundamenta Mathematicae
Similarity:
Assuming the continuum hypothesis there is an inseparable sequence of length ω₁ that contains no Lusin subsequence, while if Martin's Axiom and ¬ CH are assumed then every inseparable sequence (of length ω₁) is a union of countably many Lusin subsequences.