Parametrized Partitions of Products of Finite Sets*

For every infinite sequence of positive integers \( {\left\{ {m_{i} } \right\}}^{\infty }_{{i = 0}} \) and every Borel partition c : ω ω×[ω]ω→{0, 1} there is H∈[ω]ω and a sequence \( {\left\{ {H_{i} } \right\}}^{\infty }_{{i = 0}} \) of subsets of ω, with |H i |=m i for every i, such that c is constant on \( {\left( {{\prod\nolimits_{i = 0}^\infty {H_{i} } }} \right)}x{\left[ H \right]}^{\omega } \).

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Correspondence to C. A. Di Prisco†.

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* Research partially supported by CNRS-FONACIT Project PI 2000001471.

† This author thanks the University of Paris VII for hospitality.

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Di Prisco†, C.A., Llopis, J. & Todorcevic, S. Parametrized Partitions of Products of Finite Sets*. Combinatorica 24, 209–232 (2004).

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Mathematics Subject Classification (2000):

  • 03E02
  • 03E15
  • 05D10