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Overture: Ramsey’s Theorem

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Combinatorial Set Theory

Part of the book series: Springer Monographs in Mathematics ((SMM))

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Abstract

In this chapter, the following theorem—which can be considered as the nucleus of Ramsey Theory—will be discussed in great detail.

Theorem 2.1 (Ramsey’s Theorem). For any number n∈ω, for any positive number r∈ω, for any S∈[ω]ω, and for any colouring π: [S]n→r, there is always an H∈[S]ω such that H is homogeneous for π, i.e., the set [H]n is monochromatic.

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  1. Institut für Mathematik, Universität Zürich, Zürich, Switzerland

    Lorenz J. Halbeisen

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  1. Lorenz J. Halbeisen
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Halbeisen, L.J. (2012). Overture: Ramsey’s Theorem. In: Combinatorial Set Theory. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-4471-2173-2_2

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