**July 22**

**Tin Lok Wong**,
National University of Singapore

**Properties preserved in cofinal extensions**

Cofinal extensions generally preserve many more properties of a model of arithmetic than their sisters, end extensions. Exactly how much must or can they preserve? The answer is intimately related to how much arithmetic the model can do. I will survey what is known and what is not known about this question, and report on some recent work on this line.