Borel ideals vs. Borel sets of countable relations and trees
type: Item
instance of: scholarly article
title: Borel ideals vs. Borel sets of countable relations and trees
zbMATH Open document ID: 0673.04001
DOI: 10.1016/0168-0072(80)90003-2
author: Samy Zafrany
published in: Annals of Pure and Applied Logic
publication date: 1989-01-01T00:00:00Z
review text: For \(\mu\), a countable ordinal, let \(I_{\mu}\) be the ideal of subsets of \(\omega^{\mu}\) with order type less than \(\omega^{\mu}\). It is shown that, when appropriately coded, \(I_{\mu}\) is a \(\Sigma^ 0_{2\mu}\)-complete Borel set. This result is extended to partial orders representing small ordinals, trees with small ranks, etc. The proofs are based on Wadge games.
reviewed by: Péter Komjáth
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 28A05
zbMATH DE Number: 4101183
zbMATH Keywords: Borel classifications
zbMATH Keywords: ideal of subsets
zbMATH Keywords: Borel set
zbMATH Keywords: partial orders representing small ordinals
zbMATH Keywords: trees with small ranks
zbMATH Keywords: Wadge games
MaRDI profile type: Publication
full work available at URL: 0168-0072(80)90003-2
OpenAlex ID: W2079219288
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description: scientific article; zbMATH DE number 4101183