Logic Seminar
John Goodrick
University of Maryland
Dp-minimality and ordered groups
Abstract:
Dp-minimal theories are a subclass of dependent theories that generalize weakly minimal theories in the stable context, arising from Shelah's "dp-ranks." Dp-minimality can be defined quite simply, and in the context of ordered structures it generalizes weak o-minimality. In a divisible abelian ordered group, dp-minimality is not the same as weak o-minimality, but we show that a slight weakening of the Monotonicity Theorem holds: any definable unary function is a union of finitely many continuous, locally monotonic (partial) functions.
Tuesday January 22, 2008 at 1:00 PM in SEO 712