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

We write fin(m) and Sfin(m) for the cardinalities of the set of finite subsets and the set of permutations with finitely many non‐fixed points, respectively, of a set which is of cardinality m. In this paper, we investigate relationships between fin(m) and Sfin(m) for an infinite cardinal m in the a...

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Bibliographic Details
Published in:Mathematical logic quarterly 2021-05, Vol.67 (2), p.258-263
Main Authors: Nuntasri, Jukkrid, Panasawatwong, Supakun, Vejjajiva, Pimpen
Format: Article
Language:English
Subjects:
Permutations
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Summary:We write fin(m) and Sfin(m) for the cardinalities of the set of finite subsets and the set of permutations with finitely many non‐fixed points, respectively, of a set which is of cardinality m. In this paper, we investigate relationships between fin(m) and Sfin(m) for an infinite cardinal m in the absence of the Axiom of Choice. We give conditions that make fin(m) and Sfin(m) comparable as well as give related consistency results.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.202000058