A weird relation between two cardinals

Archive for Mathematical Logic 57 (5-6):593-599 (2018)
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Abstract

For a set M, let \\) denote the set of all finite sequences which can be formed with elements of M, and let \ denote the set of all 2-element subsets of M. Furthermore, for a set A, let Open image in new window denote the cardinality of A. It will be shown that the following statement is consistent with Zermelo–Fraenkel Set Theory \: There exists a set M such that Open image in new window and no function Open image in new window is finite-to-one.

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10.1007/s00153-017-0594-z

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Citations of this work

A Generalized Cantor Theorem In.Yinhe Peng & Guozhen Shen - 2024 - Journal of Symbolic Logic 89 (1):204-210.

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References found in this work

Consequences of arithmetic for set theory.Lorenz Halbeisen & Saharon Shelah - 1994 - Journal of Symbolic Logic 59 (1):30-40.

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