Sergio Fratarcangeli : Two generalizations of Khovanskii Theory over an o-minimal structure

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

Jan. 31, 2006, 3 p.m.

In

SEO 427

Abstract

Khovanskii Theory is an important tool for identifying new o-minimal structures and for obtaining uniformity results within o-minimal structures. In this talk, we generalize Khovanskii Theory in two directions. In one case, we produce a version that holds within any expansion of an ordered field with the intermediate value property. In the other case, we generalize how sets may be obtained from Rolle leaves---beyond mere intersections---so that the number of their connected components is still uniformly bounded.