Mathematical Sciences: Topics in Model Theory

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Pillay intends to investigate: 1) some problems in the model theory of differential fields, among them the possible existence of a superstable non-differentially closed differential field; 2) some problems involving the number of models of both countable and uncountable stable theories; 3) the possibility of defining a field in sufficiently rich o-minimal structures, and the identification of groups definable in o-minimal structures. The subarea of model theory within mathematical logic concerns itself with axiomatic systems, particularly questions about theories founded on systems of axioms, which can be answered purely from considering the forms of the axioms without real regard for their content. It is surprising how much can sometimes be learned in this way, for it often seems to be getting something for nothing. Model theorists have developed a rich subject and have been able to shed light even on such well-studied topics in algebra as the theory of groups and the theory of fields.