John Goodrick : Dp-minimality and ordered groups

Posted by , part of the Logic Seminar.

At

Jan. 22, 2008, 1 p.m.

In

SEO 712

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.