Logic(s) in the computable context

Abstract: In abstract model theory, ``logic" is typically defined as something like ``An indexed family of isomorphism-respecting partitions of the class of all structures" - or more precisely, an assignment of such partitions to signatures (usually we demand some other conditions too). But we do not always think isomorphism-invariantly; in particular, when thinking about computable structures we typically ``carve up" the universe into equivalence classes with respect to computable isomorphism.

In this talk I'll explore what there is to be said about ``abstract model theory in the computable universe." One logic we'll pay particular attention to is gotten by mixing classical computable infinitary logic with the notion of realizability coming from intuitionistic arithmetic. This is work in progress, so this talk will have lots of questions as well as results. No prior knowledge of intuitionistic logic will be assumed.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic