Mathematical Sciences: Set Theory

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S. D. Friedman's research is concerned mainly with definability problems in set theory, particularly applications of the so-called coding method invented by Ronald Jensen. Various problems and their relationship to the constructible universe of Godel and to certain other models of set theory will be considered. These models, the higher core models, will also be objects of the research themselves, both in terms of absoluteness and fine-structural properties. A postdoctoral researcher, Michael Chris Laskowski, and an advanced graduate student will be involved too. Elementary set theory is for most mathematicians simply a convenient language in which to express mathematical facts about collections of objects of various kinds. A highly developed axiomatic set theory exists, however, driven by the desire to make the foundations of mathematics absolutely secure and free from paradox of any kind. Research of this nature is in some sense mathematical hygiene, for paradoxes of the infinite abound, and mathematical intuition is not fully reliable as a protection from them.