Abstract
An induced version of the partition theorem for parameter-sets of R. L. Graham and B. L. Rothschild ( Trans. Amer. Math. Soc. 159 (1971), 257–291) is proven. This theorem generalizes the Graham-Rothschild theorem in the same way as the partition theorem for finite hypergraphs (F. G. Abramson and L. A. Harrington, J. Symblic Logic 43 (1978), 572–600 and J. Nešetřil and V. Rödl; J. Combin. Theory Ser. A 22 (1977), 289–312; 34 (1983), 183–201) generalizes Ramsey's theorem. Some applications are given, e.g., an induced version of the Rado-Folkman-Sanders theorem and an induced version of the partition theorem for finite Boolean lattices. Also it turns out that the partition theorem for finite hypergraphs is an easy consequence of the induced partition theorem for parameter-sets.
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