Combinatorial Set Theory

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The investigator proposes a program of research in axiomatic set theory. The program involves looking at a number of different questions, all of which involve combinatorial set theory and are related to large cardinals and forcing; among the areas to be studied are mutual stationarity, identity crises for large cardinals, and combinatorial principles. The techniques to be used include Radin forcing, iterated forcing and PCF theory. Combinatorial set theory is a discipline whose goal is to take familiar ideas about finite sets (such as counting, ordering and permuting) and extend them to the context of infinite sets. The theory is highly developed and has found applications in several mathematical areas where infinite sets are used, including topology and analysis. Progress on the problems which are proposed by the investigator should increase our understanding of infinite sets, and help forge tools which will be useful to set theorists and workers in other areas.