Lawvere-Tierney topologies for computability theorists

Abstract: In this talk, we study the frame of Lawvere-Tierney topologies on Hyland's effective topos. For this purpose, we introduce a new computability-theoretic reducibility notion, which is a common extension of the notions of Turing reducibility and generalized Weihrauch reducibility. Based on the work by Lee and van Oosten, we utilize this reducibility notion for providing a concrete description of the frame of the Lawvere-Tierney topologies on the effective topos. As an application, we solve several open problems proposed by Lee and van Oosten. For instance, we show that there exists no minimal Lawvere-Tierney topology which is strictly above the identity topology on the effective topos.

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.