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

Nuntasri Jukkrid | Zendy; Panasawatwong Supakun | Zendy; Vejjajiva Pimpen | Zendy

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

Author(s) -

Nuntasri Jukkrid,

Panasawatwong Supakun,

Vejjajiva Pimpen

Publication year - 2021

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.202000058

Subject(s) - mathematics , cardinality (data modeling) , consistency (knowledge bases) , set (abstract data type) , combinatorics , finite set , axiom of choice , fixed point , power set , discrete mathematics , axiom , infinite set , set theory , computer science , mathematical analysis , data mining , geometry , programming language

We write fin ( m ) andS fin ( 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 ) andS fin ( m )for an infinite cardinal m in the absence of the Axiom of Choice. We give conditions that make fin ( m ) andS fin ( m )comparable as well as give related consistency results.

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