数理逻辑研讨班：Sets definable in ordered Abelian groups of finite dp-rank and finite burden

中科院数学与系统科学研究院

数学研究所

学术报告

数理逻辑研讨班

报告人：John R. Goodrick （Universidad de los Andes）   

题  目：Sets definable in ordered Abelian groups of finite dp-rank and finite burden

时  间：2022.10.28（星期五）上午10:00-11:00

地  点：腾讯会议: 705-015-070

摘  要：In the class of NIP theories, the cardinal-valued dp-rank of a type is a useful measure of its complexity (generalizing weight in stable theories). Of particular interest are structures in which this complexity is small: dp-minimal theories (in which every nonalgebraic 1-type has dp-rank 1) and dp-finite theories (every such type has finite dp-rank). We will present some recent work (joint with Alf Dolich) on the study of definable sets in dp-finite ordered Abelian groups with particular emphasis on topological tameness properties of unary definable sets. Some results can even be established in the generality of groups with finite burden, a corresponding notion of rank for NTP₂ theories.