Mathematical Sciences: Mathematical Logic and Applications

凯斯勒研究的总主题将是发展有措施的结构的模型理论，特别是使用Loeb措施结构。他还将研究将这些模型理论方法应用于相关数学领域的可能性，特别是概率论。在逻辑编程中，库能将致力于Prolog的语义，试图构建一种声明语义与过程语义完全对应的语言。在集合论拓扑学中，库能将在马丁公理下研究可数集的组合性质。米勒将研究集合论中的各种问题。这些问题大多是关于公理集合论中的独立性和一致性结果。这意味着这个问题涉及到证明某些特定的陈述不能从集合论的通常公理中得到证明或反证。

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.