The principal investigator will continue research in model theory that falls under the two general headings of model theory for ordered structures and monadic second-order logic. In research begun several years ago, he studied the notion of an o-minimal structure. This work has unified the model theory for several specific classes of linearly ordered structures, and has yielded general results known before only in special cases. He wishes to consider several questions concerning o-minimal structures. Most importantly, he plans to attempt to develop an analogue to stability theory for linearly ordered structures, and to investigate the possibilities for a general model theory for classes of structures whose natural topology is given in a first-order way. The principal investigator also is currently engaged in writing a monograph with Y. Gurevich on monadic second-order logic for the "Perspectives in Mathematical Logic" series. This book will survey both the rich variety of methods that have been employed to prove the decidability or undecidability of the monadic second-order theory of various structures, and also the results that have been obtained using these methods. The book will be written so as to be of interest to both logicians and theoretical computer scientists.
