On compactness phenomena

12/15/2023 12:00 pm - 1:00 pm
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Member Seminar

Speaker: Alejandro Poveda

Title: On compactness phenomena

Abstract: In this presentation I shall be preoccupied with compactness phenomena in set theory. Compactness is the phenomenon by which the local properties of a mathematical structure determine its global behavior. This phenomenon is intrinsic to the very architecture of the mathematical universe and manifests to us in a cornucopia of forms. Over the past fifty years, the study of compactness phenomena has been a cornerstone of research in set theory. This talk will present recent discoveries regarding compactness principles, spanning classical themes like the tree property and stationary reflection, while also forging novel connections with other topics, such as Woodin’s HOD Conjecture.