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Some properties of infinite factorials
Mathematical Logic Quarterly 64 (3):201-206 (2018)
Abstract
With the Axiom of Choice, for any infinite cardinal but, without, we cannot conclude any relationship between and for an arbitrary infinite cardinal. In this paper, we give some properties of in the absence of and compare them to those of for an infinite cardinal. Among our results, we show that “ for any infinite cardinal and any natural number n” is provable in although “ for any infinite cardinal ” is not.Other Versions
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Citations of this work
The permutations with N non-fixed points and the sequences with length N of a set.Jukkrid Nuntasri & Pimpen Vejjajiva - 2024 - Journal of Symbolic Logic 89 (3):1067-1076.
The cardinality of the partitions of a set in the absence of the Axiom of Choice.Palagorn Phansamdaeng & Pimpen Vejjajiva - 2023 - Logic Journal of the IGPL 31 (6):1225-1231.
Factorials and the finite sequences of sets.Nattapon Sonpanow & Pimpen Vejjajiva - 2019 - Mathematical Logic Quarterly 65 (1):116-120.
Remarks on infinite factorials and cardinal subtraction in ZF$\mathsf{ZF}$.Guozhen Shen - 2022 - Mathematical Logic Quarterly 68 (1):67-73.
References found in this work
Zur Axiomatik der Mengenlehre (Fundierungs‐ und Auswahlaxiom).Ernst Specker - 1957 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 3 (13‐20):173-210.
Zur Axiomatik der Mengenlehre (Fundierungs- und Auswahlaxiom).Ernst Specker - 1957 - Mathematical Logic Quarterly 3 (13-20):173-210.
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