# Luzin Hypothesis and weak CH

1. Dec 17, 2005

### xouper

Regarding the weak continuum hypothesis (B.F. Jones):

$${\displaystyle 2^ {\aleph_{0}} < 2^ {\aleph_{1}}}$$

and the Luzin Hypothesis:

$${\displaystyle 2^ {\aleph_{0}} = 2^ {\aleph_{1}}}$$

Where can I find Bukovsky's paper that shows the Luzin Hypothesis is consistent with set theory? Or perhaps someone can repeat the proof here (or summarize it)?

Last edited: Dec 17, 2005
2. Jul 22, 2007

### xouper

3. Jul 22, 2007

### Hurkyl

Staff Emeritus
Well, a brief search lead me to

http://en.wikipedia.org/wiki/Luzin_space

and then to

http://en.wikipedia.org/wiki/Martin's_Axiom

and

http://en.wikipedia.org/wiki/Rasiowa-Sikorski_lemma

My best guess would be to start with the things that these articles reference. I've seen a few forcing arguments in topos-theoretic texts, but I don't think I've seen this one specifically.