Lusin sequences under CH and under Martin's Axiom

Volume 169 / 2001

Uri Abraham, Saharon Shelah Fundamenta Mathematicae 169 (2001), 97-103 MSC: 03E05, 03E50, 03E35. DOI: 10.4064/fm169-2-1


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.


  • Uri AbrahamDepartments of Mathematics and Computer Science
    Ben-Gurion University
    Beer-Sheva, Israel
  • Saharon ShelahInstitute of Mathematics
    The Hebrew University
    91904 Jerusalem, Israel

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