Hans Schoutens, CUNY
The model-theory of compact spaces
A more correct title would read: the model-theory of the category of compact (Hausdorff) spaces. Last year, I gave a talk about the model-theory of categories, and this talk will be its continuation (but I will repeat everything that is relevant) in which I will look at one special case: COMP, the category of compact spaces. Let C be any model that is elementary equivalent to the category COMP (but if you’re a standard guy, you can just take C=COMP and everything is still interesting). The model C 'remembers' the topology of each of its objects (except we might have lost compactness). But it can recover much more, to an extent that I would almost call it 'foundational'. I will show how to reconstruct a model of PA, a model of the ORD (ordinals) and even a model of ZFC. If you wonder, which model of ZFC you get if you just start with COMP, the answer is: the same you woke up to this morning!