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Title: Determinacy and Weakly Ramsey sets in Banach spaces
Author: Bagaria, Joan
López Abad, Jordi
Keywords: Teoria de conjunts
Espais de Banach
Applications of set theory
Descriptive set theory
Sequence spaces
Issue Date: 2002
Publisher: American Mathematical Society
Abstract: We give a sufficient condition for a set of block subspaces in an infinite-dimensional Banach space to be weakly Ramsey. Using this condition we prove that in the Levy-collapse of a Mahlo cardinal, every projective set is weakly Ramsey. This, together with a construction of W. H. Woodin, is used to show that the Axiom of Projective Determinacy implies that every projective set is weakly Ramsey. In the case of co we prove similar results for a stronger Ramsey property. And for hereditarily indecomposable spaces we show that the Axiom of Determinacy plus the Axiom of Dependent Choices imply that every set is weakly Ramsey. These results are the generalizations to the class of projective sets of some theorems from W. T. Gowers, and our paper "Weakly Ramsey sets in Banach spaces."
Note: Reproducció digital del document publicat en format paper, proporcionada per JSTOR
It is part of: Transactions of the American Mathematical Society, 2002, vol. 354, núm. 4, p. 1327-1349.
ISSN: 1088-6850
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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