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Results tagged with continuum-hypothesis
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user 82843
Questions about the continuum hypothesis, or where the continuum hypothesis or its negation plays a role. This tag is also suitable, by extension, to refer to the generalized continuum hypothesis and related issues.
20
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1
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On Erdös–Kakutani like Equivalents of the Failure of Continuum Hypothesis
Among all mysterious equivalents of the Continuum Hypothesis and its negation, there is an algebraic combinatorial equivalent of $\neg \mathit{CH}$ in Erdös and Kakutani - On non-denumerable graphs (M …
31
votes
2
answers
3k
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Mathematical Evidence Backing $|\mathbb{R}|=\aleph_2$
The "true" size of the real line, $\mathbb{R}$, has been the subject of Hilbert's first problem. Due to the Goedel and Cohen's work on the inner and outer models of $\text{ZFC}$, it turned out to be u …
CommunityBot
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2
votes
1
answer
385
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Strong Total Failures vs. Weak Instances of the Generalized Continuum Hypothesis
The exponentiation operator inflicts a subtle information loss on the transfinite numerical equations, pretty similar to the case of $a^2=b^2 \nRightarrow a=b$ in real numbers. In fact, for the infini …
CommunityBot
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3
votes
1
answer
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A Question on HOD, V and GCH
The theorem 1.1 of the following paper:
Mohammad Golshani, V, HOD, and the GCH, Journal of Symbolic Logic.
states that:
Theorem: Assume $V\models ZFC+GCH+~\text{There exists a}~(\kappa+4)-\text{str …
CommunityBot
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