Abstract: I will begin to discuss a recently submitted paper, joint with A. Dolich and C. Steinhorn, entitled "Structures having o-minimal open core". A preprint is available on my home page. This will take several meetings, so I will be the default speaker for a while whenever we don't have someone else booked. The open core of an expansion of a dense linear order is its reduct, in the sense of definability, generated by the collection of all of its open definable sets. We shall investigate expansions of dense linear orders that have o-minimal open core, with emphasis on expansions of densely ordered groups. The first main result establishes conditions under which an expansion of a densely ordered group has an o-minimal open core. The only requisite knowledge is basic definability theory and topology of ordered structures. Examples and applications will be addressed eventually, some of which will require some more sophisticated knowledge of model theory.

Notes:

Preprint available at http://www.math.ohio-state.edu/~miller [1].