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On a cardinal inequality in ZF$\mathsf {ZF}$
Mathematical Logic Quarterly (forthcoming)
Abstract
It is proved in (without the axiom of choice) that for all infinite cardinals and all natural numbers, where is the cardinality of the set of permutations with exactly non‐fixed points of a set which is of cardinality.Other Versions
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Citations of this work
Cantor’s Theorem May Fail for Finitary Partitions.Guozhen Shen - forthcoming - Journal of Symbolic Logic:1-18.
References found in this work
Factorials of infinite cardinals in zf part I: Zf results.Guozhen Shen & Jiachen Yuan - 2020 - Journal of Symbolic Logic 85 (1):224-243.
The permutations with N non-fixed points and the sequences with length N of a set.Jukkrid Nuntasri & Pimpen Vejjajiva - forthcoming - Journal of Symbolic Logic:1-10.
The well‐ordered and well‐orderable subsets of a set.John Truss - 1973 - Mathematical Logic Quarterly 19 (14‐18):211-214.
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