"First-order parts" of Weihrauch degrees
- Date: Wednesday 6 February 2019, 16:00 – 17:00
- Location: Mathematics Level 8, MALL 1, School of Mathematics
- Type: Logic, Seminars, Pure Mathematics
- Cost: Free
Keita Yokoyama, Japan Advanced Institute of Science and Technology. Part of the Logic Seminar Series.
The Weihrauch degree of a binary relation on Baire space measures the power of uniform computation of a problem defined on Baire space. In the recent studies of Weihrauch degrees, it is seen that its structure resembles the structure of second-order arithmetic in the sense of reverse mathematics. In this study, we will introduce the "first-order part" of a Weihrauch degree by focusing on numerical consequences and try to measure the first-order strength of degrees. Then we see that the first-order parts of degrees of arithmetical problems form a hierarchy corresponding to Kirby-Paris hierarchy of first-order arithmetic, and those can be classified with their first-order strength.
This is a joint work with Damir Dzhafarov and Reed Solomon.