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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.