Monochromatic Forests of Finite Subsets of N
نویسنده
چکیده
It is known that if N is finitely colored, then some color class is piecewise syndetic. (See Definition 1.1 below for a definition of piecewise syndetic.) We generalize this result by considering finite colorings of the set of all finite subsets of N . The monochromatic objects obtained are “d-copies” of arbitrary finite forests and arbitrary infinite forests of finite height. Van der Waerden’s theorem on arithmetic progressions is generalized in a similar way. Ramsey’s theorem and van der Waerden’s theorem are used in some of the proofs.
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تاریخ انتشار 2000