On Lusin's restricted continuum problem
type: Item
instance of: scholarly article
title: On Lusin's restricted continuum problem
zbMATH Open document ID: 0565.03022
DOI: 10.2307/2007070
author: Jacques Stern
published in: Annals of Mathematics. Second Series
publication date: 1984-01-01T00:00:00Z
review text: The author defines an equivalence relation E on the real line to be Lusin if all equivalence classes are Borel sets of bounded rank and E does not admit a non-empty perfect set of pairwise inequivalent elements. He defines a partition of the line into non-empty subsets to be Lusin if the corresponding equivalence relation is Lusin. A Lusin partition is countable if it admits at most countable many members. The author proves that in Solovay's model (in which every set of reals is Lebesgue measurable) any Lusin partition is countable; and that if for all \(\alpha\), \(\aleph_ 1^{L(\alpha)}<\aleph_ 1\), then any Lusin partition, whose corresponding equivalence relation is \(\Delta^ 1_ 2\), is countable.
Mathematics Subject Classification ID: 03E15
zbMATH DE Number: 3900738
zbMATH Keywords: equivalence relation
zbMATH Keywords: partition of the line
zbMATH Keywords: Lusin partition
zbMATH Keywords: Solovay's model
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2007070
OpenAlex ID: W1991271290
description: scientific article; zbMATH DE number 3900738