abstract


A weird relation between two cardinals

Lorenz Halbeisen


For a set M, let seq(M) denote the set of all finite sequences which can be formed with elements of M, and let {M,M} denote the set of all 2-element subsets of M. It will be shown that the following statement is consistent with Zermelo-Fraenkel Set Theory ZF: There exists a set M such that the cardinality of seq(M) is strictly smaller than the cardinality of {M,M} and no function from {M,M} to seq(M) is finite-to-one.

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