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A cardinal defined by a polarized partition relation

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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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Authors and Affiliations

  1. Department of Mathematics, Instituto Venezolano de Investigaciones Científicas, Apartado 21827, 1020-A, Caracas, Venezuela

    Carlos Gugusto Di Prisco & Stevo Todorcevic

  2. Department of Mathematics, University of Toronto, Toronto, Canada

    Stevo Todorcevic

  3. Mathematical Institute of the Serbian Academy of Science, Serbia

    Stevo Todorcevic

Authors
  1. Carlos Gugusto Di Prisco
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  2. Stevo Todorcevic
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Correspondence to Carlos Gugusto Di Prisco.

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Di Prisco, C.G., Todorcevic, S. A cardinal defined by a polarized partition relation. Isr. J. Math. 109, 41–52 (1999). https://doi.org/10.1007/BF02775025

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  • DOI: https://doi.org/10.1007/BF02775025

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