The goal of the seminar in S1 of 2018 is to understand classifying topoi. These are topoi which have a universal property with respect to a particular geometry theory, and they are constructed as categories of sheaves on a site, the underlying category of which is defined in terms of the language of the theory. We have just had two lectures by Patrick Elliott on categories of sheaves, so it is time to look more closely at the relationship between topoi and higher-order logic. This talk by Will Troiani is an introduction to this theme. He explains how to think about predicates in general topoi, and uses that as a way to introduce elementary topoi and prove that this definition is an equivalent characterisation of topoi within all categories.
The lecture notes are available here: therisingsea.org/notes/ch2018-lecture8.pdf.
For the general seminar webpage see therisingsea.org/post/seminar-ch/.