In order to generalize Poizat’s theory of belle paires to unstable theories, one needs to assume the amalga-
mation property for the class of global definable types.
In the talk, we will highlight this connection and exhibit some important classes of theories in which de-
finable types may be amalgamated. We will also exhibit an example (which has TP2) of a theory in which
definable types may not be amalgamated and sketch the construction of a candidate NIP example with the
same behavior.
This talk is based on joint work with Pablo Cubides and Jinhe Ye, and with Rosario Mennuni.