Logic Seminar
Chris Shaw
Columbia College
Skolem functions for a class of weakly o-minimal structures
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.
Tea at 2:30pm in SEO 300
Tuesday April 19, 2011 at 3:00 PM in SEO 612