Axioms of determinacy and biorthogonal systems
type: Item
instance of: scholarly article
title: Axioms of determinacy and biorthogonal systems
zbMATH Open document ID: 0712.46004
DOI: 10.1007/BF02764903
author: Alain Louveau
author: Gilles Godefroy
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let X be a norm-closed and not norm-separable subspace of \(\ell^{\infty}({\mathbb{N}})\). The authors study the question of whether X contains a biorthogonal system of cardinality \(2^{\aleph_ 0}\). The answer depends on the set theory which is used. For example, if X is in the projective hierarchy with respect to the \(w^*\)-topology [i.e. in \(\Sigma^ 1_{n+1}\), cf. \textit{Y. N. Moschovakis}, Descriptive Set Theory, Amsterdam (1980; Zbl 0433.03025)] then the answer is in the affirmative provided one assumes that all \(\Pi^ 1_ n\) games on the integers are determined.
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 54H05
Mathematics Subject Classification ID: 03E15
zbMATH DE Number: 4171690
zbMATH Keywords: axioms of determinacy
zbMATH Keywords: biorthogonal system
reviewed by: Martin Schottenloher
MaRDI profile type: Publication
Wikidata QID: Q114693404
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full work available at URL: https://doi.org/10.1007/bf02764903
OpenAlex ID: W1964285693
description: scientific article; zbMATH DE number 4171690