G-compactness, hereditary G-compactness and related phenomena
The notion of G-compactness, along with the Galois groups, was introduced by Lascar in order to find a sufficient condition under which a first order theory can be recovered from the category of its models.
I will recall this notion. In order to do that, I will also recall various classical notions of strong types, and possibly the Galois group of the theory (and briefly discuss their importance).
Then I will introduce the stronger notion of hereditary G-compactness, which is a property of a first order theory (most likely strictly) weaker than simplicity, and hence stability.
Depending on the available time, I might do some of the following (not necessarily in this order):
- discuss the relation with connected group components,
- show some examples of drastic failure of heredity for G-compactness,
- show that a theory which interprets an infinite linear order is not hereditarily G-compact (which, modulo an open conjecture, implies that an NIP theory is stable if and only if it is hereditarily G-compact),
- discuss possible examples of hereditarily G-compact theories which are not simple.
Wed, 03/04/2019 - 11:00 to 13:00