The structure of Weihrauch degrees - what we know and what we don't know

Abstract: The Weihrauch degrees are a popular setting for classifying the computational content of mathematical theorems. Understanding their structure is useful as technical tool in concrete classifications. Moreover, their structure tells us something about how degrees of non-computability look like in principle. In this talk, I'll summarize what is already known about the structure of the Weihrauch degrees, and try to draw attention to some open problems. For example. we know that they form a distributive lattice, which is not a Heyting algebra and which is not complete. We have further natural algebraic operations, and we know of a few that they are definable in terms of others. The Medvedev degrees embed into the Weihrauch degrees as a lattice, as do the many-one degrees (but in a weird way).

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.