Abstract: The puzzling logic (called
With Väänänen, we introduced the first approximation (called ,) as a variant of with a transparent syntax and many of the strong properties of Shelah’s logic.
The second approximation (called Chain Logic), while not new (it is due to Karp), has been revisited recently by Dzamonja and Väänänen) also in relation to Shelah’s and the Interpolation property.
I will provide a description of these three logics, with emphasis on their relevance to model theory.
As a bonus, I will make a connection between these logics and axiomatizing correctly an arbitrary AEC. This last part is joint work with Shelah.