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Model Theory Seminar
Chris Shaw
Columbia College Chicago
Title: Ordered Structures, o-minimality, and definable choice

Abstract: Given that any o-minimal densely ordered group has full definable choice (namely, definable Skolem functions and uniform elimination of imaginaries), it is a natural question to ask whether this can be achieved in the weakly o-minimal setting. We examine the case of a structure N obtained by adding a new convex predicate to an o-minimal structure M. If the new predicate is interpreted by a bounded convex set with endpoints outside of M, then the resulting structure is properly weakly o-minimal and has a weakly o-minimal theory. We show that in this case, definable Skolem functions are present precisely when N has a definable subgroup. Together with a simple application of compactness, this yields the result that no such structure may have full definable choice.

Date: Monday, March 14, 2011
Time: 5:00 pm
Location: Wean Hall 8220
Submitted by:  Grossberg