We can never see the forest - James Carr Progress Review 2

An important limitation of classical first-order logic is its locality. Whether a formula is modelled in a classical structure depends only on its behaviour at a 'local' level, with the consequence that first-order logic cannot express global properties. Made precise through a number of locality theorems - most famously Hanf and Gaifman locality - this has a number of useful applications to theoretical computer science especially in the topic of definability and complexity.

In this talk, we explore the task of generalising locality to the many-valued setting, giving an overview of what centers the generalisation and an example of a toy application. This then provides a springboard to a reflection on the metamathematical question of what constitutes interesting mathematical research.