# FOM: Luzin hypothesis

Kanovei kanovei at wminf2.math.uni-wuppertal.de
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
consideration.