A cardinal defined by a polarized partition relation |
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| Authors: | Carlos Gugusto Di Prisco Stevo Todorcevic |
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| Institution: | (1) Department of Mathematics, Instituto Venezolano de Investigaciones Científicas, Apartado 21827, 1020-A Caracas, Venezuela;(2) Department of Mathematics, University of Toronto, Toronto, Canada;(3) Mathematical Institute of the Serbian Academy of Science, Serbia |
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| Abstract: | We study the first cardinalκ satisfying a partition relation defined on the set of finite sequences of smaller ordinals. We show that the fact that this
cardinal is ℵω is equiconsistent with the existence of a measurable cardinal. Under GCH, this cardinal must be inaccessible if it has uncountable
cofinality. It is shown that the GCH assumption is necessary here. |
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