Translator Disclaimer
August 2021 A Choice-Free Cardinal Equality
Guozhen Shen
Author Affiliations +
Notre Dame J. Formal Logic 62(3): 577-587 (August 2021). DOI: 10.1215/00294527-2021-0028

Abstract

For a cardinal a, let fin(a) be the cardinality of the set of all finite subsets of a set which is of cardinality a. It is proved without the aid of the axiom of choice that, for all infinite cardinals a and all natural numbers n,

2fin(a)n=2[fin(a)]n.

On the other hand, it is proved consistent with ZF that there exists an infinite cardinal a such that

2fin(a)<2fin(a)2<2fin(a)3<<2fin(fin(a)).

Citation

Download Citation

Guozhen Shen. "A Choice-Free Cardinal Equality." Notre Dame J. Formal Logic 62 (3) 577 - 587, August 2021. https://doi.org/10.1215/00294527-2021-0028

Information

Received: 6 March 2020; Accepted: 20 May 2021; Published: August 2021
First available in Project Euclid: 6 October 2021

Digital Object Identifier: 10.1215/00294527-2021-0028

Subjects:
Primary: 03E10
Secondary: 03E25

Rights: Copyright © 2021 University of Notre Dame

JOURNAL ARTICLE
11 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.62 • No. 3 • August 2021
Back to Top