• Source: Second continuum hypothesis

The second continuum hypothesis, also called Luzin's hypothesis or Luzin's second continuum hypothesis, is the hypothesis that




2


ℵ

0




=

2


ℵ

1






{\displaystyle 2^{\aleph _{0}}=2^{\aleph _{1}}}

. It is the negation of a weakened form,




2


ℵ

0




<

2


ℵ

1






{\displaystyle 2^{\aleph _{0}}<2^{\aleph _{1}}}

, of the Continuum Hypothesis (CH). It was discussed by Nikolai Luzin in 1935, although he did not claim to be the first to postulate it.: 157, 171 : §3 : 130–131  The statement




2


ℵ

0




<

2


ℵ

1






{\displaystyle 2^{\aleph _{0}}<2^{\aleph _{1}}}

may also be called Luzin's hypothesis.
The second continuum hypothesis is independent of Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC): its truth is consistent with ZFC since it is true in Cohen's model of ZFC with the negation of the Continuum Hypothesis;: 109–110  its falsity is also consistent since it is contradicted by the Continuum Hypothesis, which follows from V=L. It is implied by Martin's Axiom together with the negation of the CH.




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References

Kata Kunci Pencarian:

• Bahasa Sanskerta
• Yesus
• Ateisme
• Evolusi
• Hubungan Romawi dengan Tiongkok
• Second continuum hypothesis
• Continuum hypothesis
• Weak continuum hypothesis
• Cardinality of the continuum
• Beth number
• Constructible universe
• Spacetime
• Freiling's axiom of symmetry
• Martin's axiom
• Simulation hypothesis