Year: 2021
Type: article
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)).
Author: Guozhen Shen
Institution: Wuhan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2996905922