题目：Open Cores in Hrushovski Constructions

报告人：张祎龙，波恩大学

时间：2026年11月18日（周三）下午14:00-15:00

地点：新楼308

摘要：A central problem in model theory is to understand the complexity of definable sets. For a topological structure, the open core measures its topological complexity—namely, the complexity of its open definable sets. In this talk, I will introduce the Boxall–Hieronymi criterion for an expansion to preserve the open core. Using this criterion, I will outline a proof that dense pairs of o-minimal structures have o-minimal open cores. Turning to my own work, I will present raising to powers on the unit circle, a new structure obtained via the Hrushovski construction. Hrushovski constructions come equipped with a pregeometry, which is the main reason that the resulting structures have o-minimal open cores.