Infinitary Ramsey Theory

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ABSTRACTThe first direction of the research will be an investigation of the ordinary partition relation and the polarized partition with exponents 2 and 1,1 respectively. The second direction will be the continuation of a long and fruitful collaboration with Peter Komjath. The investigators will work on the following topics: Square bracket partition relations for order types, the simultaneous chromatic number and splitting of graphs, and the obligatory finite subsystems of large chromatic set systems. The PI will collaborate on compact scattered spaces with Istvan Juhasz:The award will also contain Visitor Support, which the continues a very successfull visitor program. Pofessor Saharon Shelah regularly spends the months September and October at the Rutgers Mathematics Department. Many logicians come to work with him on their problems.