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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/7783
Determinacy and Weakly Ramsey sets in Banach spaces
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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."
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BAGARIA, Joan i LÓPEZ ABAD, Jordi. Determinacy and Weakly Ramsey sets in Banach spaces. Transactions of the American Mathematical Society. 2002. Vol. 354, núm. 4, pàgs. 1327-1349. ISSN 1088-6850. [consulta: 10 de maig de 2026]. Disponible a: https://hdl.handle.net/2445/7783