Factorials and the finite sequences of sets

descriptionPublicationkeyboard_double_arrow_right Article 26 Apr 2019 English Publisher:WileyJournal:Mathematical Logic Quarterly, volume 65, pages 116-120 (issn: 0942-5616, eissn: 1521-3870,

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Authors: Nattapon Sonpanow; Pimpen Vejjajiva;

doi: 10.1002/malq.201800052

Factorials and the finite sequences of sets

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Abstract

AbstractWe 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 .

Related Organizations

Chulalongkorn University
Thailand

Keywords

Axiom of choice and related propositions, Consistency and independence results

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