**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.

## Date:

Wed, 03/04/2019 - 11:00 to 13:00

## Location:

Ross 63