Mathematical Sciences: Mathematical Logic and Applications

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The general theme of Keisler's research will be to develop the model theory of structures with measures, particularly using the Loeb measure construction. He will also study the possibilities of applying these model theoretic methods to related areas of mathematics, particularly probability theory. In logic programming, Kunen will work on the semantics of Prolog, attempting to construct a language in which the declarative semantics corresponds exactly to the procedural semantics. In set-theoretic topology, Kunen will study combinatorial properties of countable sets under Martin's Axiom. Miller will work on various problems in set theory. Most of these problems are about independence and consistency results in axiomatic set theory. This means that the problem involves showing some particular statement cannot be proved or disproved from the usual axioms of set theory.