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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.
2
votes
1
answer
385
views
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 …
3
votes
1
answer
442
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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 …
20
votes
1
answer
1k
views
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
views
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 …