The dual Cantor-Bernstein theorem and the partition principle
type: Item
instance of: scholarly article
title: The dual Cantor-Bernstein theorem and the partition principle
zbMATH Open document ID: 0716.03044
author: Gregory H. Moore
author: Bernhard Banaschewski
published in: Notre Dame Journal of Formal Logic
publication date: 1990-01-01T00:00:00Z
review text: The authors give another proof of the Banaschewski and Brümmer theorem [\textit{B. Banaschewski} and \textit{G. C. L. Brümmer}, Quaest. Math. 9, 1- 27 (1986; Zbl 0604.18002)] that a strong form of the Cantor-Bernstein theorem which is formulated in terms of the surjective ordering of cardinalities, is equivalent to the axiom of choice. They also compare the relative positions of variants of this theorem and variants of the partition principle in the hierarchy of the choice principles and present a historical account of these variants.
Mathematics Subject Classification ID: 03E25
zbMATH DE Number: 4179369
zbMATH Keywords: hierarchy of choice principles
zbMATH Keywords: Cantor-Bernstein theorem
zbMATH Keywords: surjective ordering of cardinalities
zbMATH Keywords: axiom of choice
zbMATH Keywords: partition principle
reviewed by: Norbert Brunner
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093635502
OpenAlex ID: W2028165102
Wikidata QID: Q59485432
DBLP publication ID: journals/ndjfl/BanaschewskiM90
DOI: 10.1305/NDJFL/1093635502
description: scientific article; zbMATH DE number 4179369