FOM: Luzin hypothesis

Kanovei kanovei at
Mon Oct 19 10:24:53 EDT 1998

Thomas Forster wrote

>I haven't been keeping up with this, so this might be repetitious
>ort tardy.  Didn't Luzin have a hypothesis that $2^{\elaph_0} =
>2^{\aleph_1}$.   And why did he conjecture this? 

Luzin mentioned the hypothesis near the end of 20s, it was known 
as Lusin continuum hypothesis. There is more in my paper in 
Russian Math Surveys 1995, 40, no 3, and Uspensky's article in 
the same volume. 
The LCH is a consequence of some other hypotheses which Luzin 
was interested in, e.g. that any union of $\aleph_1$ many Borel 
sets is A_2 -- this is I think why LSC also came into 

Vladimir Kanovei

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