Lusin sequences under CH and under Martin's Axiom

1998/07/15 by Uri Abraham, Saharon Shelah, Abraham, Uri +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO

paper · pdf · doi:10.48550/arxiv.math/9807178

published as Fund. Math. 169 No. 2 (2001) 97--103

arxiv created 1998/07/15 · openalex publication_date 1998/07/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Assuming the continuum hypothesis there is an inseparable sequence of length omega₁ that contains no Lusin subsequence, while if Martin's Axiom and the negation of CH is assumed then every inseparable sequence (of length omega₁) is a union of countably many Lusin subsequences.

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