The power set and the set of permutations with finitely many non‐fixed points of a set

Mathematical Logic Quarterly 69 (1):40-45 (2023)
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Abstract

For a cardinal, we write for the cardinality of the set of permutations with finitely many non‐fixed points of a set which is of cardinality. We investigate the relationships between and for an arbitrary infinite cardinal in (without the axiom of choice). It is proved in that for all infinite cardinals, and we show that this is the best possible result.

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10.1002/malq.202100070

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Citations of this work

Cantor’s Theorem May Fail for Finitary Partitions.Guozhen Shen - forthcoming - Journal of Symbolic Logic:1-18.

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References found in this work

Factorials and the finite sequences of sets.Nattapon Sonpanow & Pimpen Vejjajiva - 2019 - Mathematical Logic Quarterly 65 (1):116-120.
Consequences of arithmetic for set theory.Lorenz Halbeisen & Saharon Shelah - 1994 - Journal of Symbolic Logic 59 (1):30-40.

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