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A weird relation between two cardinals
Archive for Mathematical Logic 57 (5-6):593-599 (2018)
Abstract
For a set M, let \\) denote the set of all finite sequences which can be formed with elements of M, and let \ denote the set of all 2-element subsets of M. Furthermore, for a set A, let Open image in new window denote the cardinality of A. It will be shown that the following statement is consistent with Zermelo–Fraenkel Set Theory \: There exists a set M such that Open image in new window and no function Open image in new window is finite-to-one.Other Versions
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Citations of this work
A Generalized Cantor Theorem In.Yinhe Peng & Guozhen Shen - 2024 - Journal of Symbolic Logic 89 (1):204-210.
Remarks on infinite factorials and cardinal subtraction in ZF$\mathsf{ZF}$.Guozhen Shen - 2022 - Mathematical Logic Quarterly 68 (1):67-73.
Four cardinals and their relations in ZF.Lorenz Halbeisen, Riccardo Plati, Salome Schumacher & Saharon Shelah - 2023 - Annals of Pure and Applied Logic 174 (2):103200.
References found in this work
Consequences of arithmetic for set theory.Lorenz Halbeisen & Saharon Shelah - 1994 - Journal of Symbolic Logic 59 (1):30-40.
Relations between some cardinals in the absence of the axiom of choice.Lorenz Halbeisen & Saharon Shelah - 2001 - Bulletin of Symbolic Logic 7 (2):237-261.
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