The strength of the \(\Delta\)-system lemma
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.
scientific article; zbMATH DE number 440190
scientific article