The strength of the \(\Delta\)-system lemma
type: Item
instance of: scholarly article
title: The strength of the \(\Delta\)-system lemma
zbMATH Open document ID: 0781.03037
author: Jeffrey Solski
author: Paul Howard
published in: Notre Dame Journal of Formal Logic
publication date: 1993-12-06T00:00:00Z
review text: It is shown that the \(\Delta\)-system lemma is not implied by the axiom of choice nor does it imply the axiom of choice. It is also shown that the \(\Delta\)-system lemma is equivalent (in set theory without the axiom of choice) to the conjunction of the countable union theorem and the assertion that every uncountable collection of countable sets has an uncountable subcollection with a choice function.
Mathematics Subject Classification ID: 03E25
zbMATH DE Number: 440190
zbMATH Keywords: \(\Delta\)-system lemma
zbMATH Keywords: axiom of choice
zbMATH Keywords: countable union theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093634567
OpenAlex ID: W1986894712
Wikidata QID: Q124802928
DOI: 10.1305/NDJFL/1093634567
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description: scientific article; zbMATH DE number 440190