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By RAMSEY’S THEOREM 4.0, for every 2-colouring of [ω]2 there is a homogeneous set; on the other hand we have seen that there are 2-colourings of [ω]ω without a homogeneous set (see the example given in Chapter 4).

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The Shattering Number Revisited

  • 章节

  • 发表日期：

    2025年

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  • Lorenz J. Halbeisen

摘要

By RAMSEY’S THEOREM 4.0, for every 2-colouring of [ω]2 there is a homogeneous set; on the other hand we have seen that there are 2-colourings of [ω]ω without a homogeneous set (see the example given in Chapter 4).