Jouko Väänänen, University of Helsinki
Stationary logic and set theory
Stationary logic was introduced in the 1970’s. It allows the quantifier 'for almost all countable subsets s…'. Although it is undoubtedly a kind of second order logic, it is completely axiomatizable, countably compact and satisfies a kind of Downward Lowenheim-Skolem theorem. In this talk I give first a general introduction to the extension of first order logic by this 'almost all'-quantifier. As 'almost all' is interpreted as 'for a club of', the theory of this logic is entangled with properties of stationary sets. I will give some examples of this. The main reason to focus on this logic in my talk is to use it to build an inner model of set theory. I will give a general introduction to this inner model, called C(aa), or the aa-model, and sketch a proof of CH in the model. My work on the aa-model is joint work with Juliette Kennedy and Menachem Magidor.