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Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.
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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 …