Factorials and the finite sequences of sets

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Mathematical Logic Quarterly 65 (1):116-120 (2019)
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Abstract

We write for the cardinality of the set of finite sequences of a set which is of cardinality. With the Axiom of Choice (), for every infinite cardinal where is the cardinality of the permutations on a set which is of cardinality. In this paper, we show that “ for every cardinal ” is provable in and this is the best possible result in the absence of. Similar results are also obtained for : the cardinality of the set of finite sequences without repetition of a set which is of cardinality.

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10.1002/malq.201800052

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References found in this work

Zur Axiomatik der Mengenlehre (Fundierungs‐ und Auswahlaxiom).Ernst Specker - 1957 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 3 (13‐20):173-210.
Some properties of infinite factorials.Nattapon Sonpanow & Pimpen Vejjajiva - 2018 - Mathematical Logic Quarterly 64 (3):201-206.
Consequences of arithmetic for set theory.Lorenz Halbeisen & Saharon Shelah - 1994 - Journal of Symbolic Logic 59 (1):30-40.
Zur Axiomatik der Mengenlehre (Fundierungs- und Auswahlaxiom).Ernst Specker - 1957 - Mathematical Logic Quarterly 3 (13-20):173-210.

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