On Borel ideals
type: Item
instance of: scholarly article
title: On Borel ideals
zbMATH Open document ID: 0822.03026
DOI: 10.1016/0168-0072(94)90029-9
author: Fons van Engelen
published in: Annals of Pure and Applied Logic
publication date: 1995-01-09T00:00:00Z
review text: In the main theorem it is shown that for every first category homogeneous Borel subspace of \({\mathcal P} (\omega)\) the following conditions are equivalent: (i) \(X\) can be embedded in \({\mathcal P} (\omega)\) as an ideal on \(\omega\); (ii) \(X\) is homeomorphic to \(X\times X\); (iii) \(X\) is Wadge- equivalent to \(X\times X\). Moreover, using the Wadge classes [cf. \textit{A. Louveau}, Cabal Semin. 79-81, Lect. Notes Math. 1019, 28-55 (1983; Zbl 0535.03026)] the author obtains a description of possible Wadge classes for Borel ideals on \(\omega\).
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 03E05
zbMATH DE Number: 706879
zbMATH Keywords: homogeneous set
zbMATH Keywords: Borel set
zbMATH Keywords: Wadge equivalent sets
zbMATH Keywords: Vietoris topology
zbMATH Keywords: Wadge classes
zbMATH Keywords: Borel ideals
reviewed by: Tomasz Natkaniec
MaRDI profile type: Publication
full work available at URL: 0168-0072(94)90029-9
OpenAlex ID: W1995907534
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description: scientific article; zbMATH DE number 706879