Lawvere-Tierney topologies for computability theorists

06/06/2021
by   Takayuki Kihara, et al.
0

In this article, we introduce certain kinds of computable reduction games with imperfect information. One can view such a game as an extension of the notion of Turing reduction, and generalized Weihrauch reduction as well. Based on the work by Lee and van Oosten, we utilize these games for providing a concrete description of the lattice of the Lawvere-Tierney topologies on the effective topos (equivalently, the subtoposes of the effective topos preordered by geometric inclusion). As an application, for instance, we show that there exists no minimal Lawvere-Tierney topology which is strictly above the identity topology on the effective topos.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset