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May 2020 A Note on Strongly Almost Disjoint Families
Guozhen Shen
Notre Dame J. Formal Logic 61(2): 227-231 (May 2020). DOI: 10.1215/00294527-2020-0002

Abstract

For a set M, let |M| denote the cardinality of M. A family F is called strongly almost disjoint if there is an nω such that |AB|<n for any two distinct elements A, B of F. It is shown in ZF (without the axiom of choice) that, for all infinite sets M and all strongly almost disjoint families FP(M), |F|<|P(M)| and there are no finite-to-one functions from P(M) into F, where P(M) denotes the power set of M.

Citation

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Guozhen Shen. "A Note on Strongly Almost Disjoint Families." Notre Dame J. Formal Logic 61 (2) 227 - 231, May 2020. https://doi.org/10.1215/00294527-2020-0002

Information

Received: 28 November 2018; Accepted: 27 July 2019; Published: May 2020
First available in Project Euclid: 14 February 2020

zbMATH: 07222688
MathSciNet: MR4092532
Digital Object Identifier: 10.1215/00294527-2020-0002

Subjects:
Primary: 03E10
Secondary: 03E25

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 2 • May 2020
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