Chris Shaw : Skolem functions for a class of weakly o-minimal structures

Posted by , part of the Logic Seminar.

At

April 19, 2011, 3 p.m.

In

SEO 612

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 M' obtained by adding a new convex predicate to an o-minimal structure M. If the new predicate is interpreted by a convex set bounded on at least one side with an endpoint outside of M, then the resulting structure is properly weakly o-minimal and has a weakly o-minimal theory. In this case, modulo some definable elements, M' has definable Skolem functions present precisely when M' is valuational.

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