Research in Model Theory: Generic Structures

Northern Illinois University, Dekalb IL

Investigators

Abstract

Abstract Award: DMS-0203747 Principal Investigator: Kitty L. Holland Holland's proposed work centers on applying the Hrushovski-style amalgamation technique to produce novel examples of omega-stable structures. Together with Baldwin, Holland is engaged in an attempt to use this technique to produce a bad field. Holland's work toward this end has produced algebro-geometric results of independent interest on the relationship between transcendence degree and multiplicative group rank in characteristic zero fields. Holland proposes to exploit this work to complete the bad field project with Baldwin and to extend the algebro-geometric results. She further proposes to settle stability questions for certain structures produced by the technique; to analyze the geometries of structures produced by the technique and to extend her joint work with Baldwin toward an abstract model theoretic analysis of the technique and its products. Since its introduction in the early 90s, Hrushovski's amalgamation technique has been applied with great success to settle a variety of old existence conjectures central to algebraic model theory. Holland's ambition, embodied in this proposal, is threefold: To continue breaking new ground in application of the technique, to explore the limitations of the technique by characterizing common properties of its products, and to make the technique more widely and efficiently applicable by extracting common difficulties arising in its implementation and dealing with them uniformly on an abstract level. Holland's proposed work centers on applying the Hrushovski-style amalgamation technique to produce novel examples of omega-stable structures. Together with Baldwin, Holland is engaged in an attempt to use this technique to produce a bad field. Holland's work toward this end has produced algebro-geometric results of independent interest on the relationship between transcendence degree and multiplicative group rank in characteristic zero fields. Holland proposes to exploit this work to complete the bad field project with Baldwin and to extend the algebro-geometric results. She further proposes to settle stability questions for certain structures produced by the technique; to analyze the geometries of structures produced by the technique and to extend her joint work with Baldwin toward an abstract model theoretic analysis of the technique and its products. Since its introduction in the early 90s, Hrushovski's amalgamation technique has been applied with great success to settle a variety of old existence conjectures central to algebraic model theory. Holland's ambition, embodied in this proposal, is threefold: To continue breaking new ground in application of the technique, to explore the limitations of the technique by characterizing common properties of its products, and to make the technique more widely and efficiently applicable by extracting common difficulties arising in its implementation and dealing with them uniformly on an abstract level.