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Coda: A Dual Form of 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 we shall present some results in dual Ramsey Theory, i.e., Ramsey type results dealing with partitions of ω. The word “dual” is motivated by the following fact: Each infinite subset of ω corresponds to the image of an injective function from ω into ω, whereas each infinite partition of ω corresponds to the set of pre-images of elements of ω of a surjective function from ω onto ω. Similarly, n-element subsets of ω correspond to images of injective functions from n into ω, whereas n-block partitions of ω correspond to pre-images of surjective functions from ω onto n. Thus, to some extent, subsets of ω and partitions of ω are dual to each other.

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

    Lorenz J. Halbeisen

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Halbeisen, L.J. (2012). Coda: A Dual Form of Ramsey’s Theorem. In: Combinatorial Set Theory. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-4471-2173-2_11

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