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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the characterization of Souslin and Borel sets

Author: R.-D. Reiss
Journal: Proc. Amer. Math. Soc. 53 (1975), 530-534
MSC: Primary 54H05; Secondary 04A15
MathSciNet review: 0385827
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Abstract: Let $ \mathfrak{X}$ be an arbitrary family of sets in the basic set $ X$. In this paper Souslin- $ \mathfrak{X}$ sets are represented as projections on $ X$ of certain $ \sigma \delta $-sets in the cartesian product space of $ X$ and the Baire space (or $ X$ and the real line). For $ L{\text{ - }}\mathfrak{X}$ sets (i.e. Souslin sets defined with disjoint unions; ensembles d'unicité) injective projections are considered. The results also apply to Borel- $ \mathfrak{X}$ sets since the system of $ L{\text{ - }}\mathfrak{X}$ sets includes the Borel- $ \mathfrak{X}$ sets under suitable conditions.

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PII: S 0002-9939(1975)0385827-2
Keywords: Souslin sets, Borel sets, $ \sigma \delta $-sets, injective projections
Article copyright: © Copyright 1975 American Mathematical Society

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