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### Solutions to the Continuum Hypothesis

(A related MO question: What is the general opinion on the Generalized Continuum Hypothesis? )
Background
The Continuum Hypothesis (CH) posed by Cantor in 1890 asserts that $ \aleph_1=2^{\aleph_0}$. ...

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### Making all cardinals countable and its HOD

Suppose that $G$ is $Col(\omega, <Ord)$-generic over $V$ and let $W=HOD^{V[G]}$. Is $CH$ true in $W$? In general, what can we say about the behaviour of the power function in $W$?
Update. Are the ...

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### Very Large Cardinal Axioms and Continuum Hypothesis

Are very large cardinal axioms like $I_0$, $I_1$, $I_2$ consistent with $CH$ and $GCH$?

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### Are all models of ZF + DC + “All set of reals are lebesgue measurable” also models of CH? [duplicate]

Possible Duplicate:
Lebesgue Measurability and Weak CH
I have studied a little set theory and I found that Solovay constructed a model of ZF+DC+"All set of reals are Lebesgue measurable" and ...