# Understanding genericity for cuts

## Tin Lok Wong

### Ghent University

In a nonstandard model of arithmetic, initial segments with no maximum elements are traditionally called *cuts*. It is known that even if we restrict our attention to cuts that are closed under a fixed family of functions (e.g., multiplication, the primitive recursive functions, or the Skolem functions), the properties of cuts can still vary greatly. I will talk about what *genericity* means amongst such great variety. This notion of genericity comes from a version of model theoretic forcing devised by Richard Kaye in his 2008 paper. Some ideas were already implicit in the work by Laurence Kirby and Jeff Paris on indicators in the 1970s.

Tin Lok Wong is currently a Postdoctoral Researcher at Ghent University, Belgium, where he is part of the Philosophical Frontiers in Reverse Mathematics project, led by Sam Sanders from Ghent and Keita Yokoyama from Tokyo Institute of Technology, Japan. His research mainly concerns in the model theory of arithmetic, with other interests including various parts of mathematical logic, theoretical computer science, philosophy of mathematics, algebra, and combinatorics. Before arriving at Ghent, he was a Research Fellow at the National University of Singapore, working with Professor Chitat Chong and Associate Professor Yue Yang. His PhD degree comes from the University of Birmingham, UK, where his thesis supervisor was Dr. Richard Kaye.