Is Luzin Hypothesis Consistent with Set Theory?

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The discussion centers on the Luzin Hypothesis, which posits that 2^ℵ₀ equals 2^ℵ₁, contrasting with the weak continuum hypothesis that states 2^ℵ₀ is less than 2^ℵ₁. Participants seek Bukovsky's paper demonstrating the consistency of the Luzin Hypothesis with set theory and express interest in a summary or proof of the concept. They reference Wikipedia articles on Luzin space, Martin's Axiom, and the Rasiowa-Sikorski lemma as potential starting points for further exploration. There is mention of forcing arguments found in topos-theoretic literature, although specific references to the Luzin Hypothesis are lacking. The conversation highlights a gap in accessible resources for understanding the consistency of the Luzin Hypothesis within set theory.
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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)?
 
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