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Remarks on infinite factorials and cardinal subtraction in ZF$\mathsf{ZF}$
Mathematical Logic Quarterly 68 (1):67-73 (2022)
Abstract
The factorial of a cardinal, denoted by, is the cardinality of the set of all permutations of a set which is of cardinality. We give a condition that makes the cardinal equality provable without the axiom of choice. In fact, we prove in that, for all cardinals, if and there is a permutation without fixed points on a set which is of cardinality, then.Other Versions
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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.
Factorials of infinite cardinals in zf part II: Consistency results.Guozhen Shen & Jiachen Yuan - 2020 - Journal of Symbolic Logic 85 (1):244-270.
Some properties of infinite factorials.Nattapon Sonpanow & Pimpen Vejjajiva - 2018 - Mathematical Logic Quarterly 64 (3):201-206.
A weird relation between two cardinals.Lorenz Halbeisen - 2018 - Archive for Mathematical Logic 57 (5-6):593-599.
Generalizations of Cantor's theorem in ZF.Guozhen Shen - 2017 - Mathematical Logic Quarterly 63 (5):428-436.
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