Simple theories

Group configurations and germs in simple theories

“…We assume familiarity with the basic definitions and properties regarding simple theories, as given in [Kim98a,KP97], as well as with hyperimaginaries and canonical bases, as given in [HKP00] or [Wag00]. Convention 1.1.…”

Supersimple theories

“…The basic material on simple theories is from [16], [7], [12] and also [1] for low theories. The material on hyperimaginaries and canonical bases is from [4] and [13].…”

“…(See also [8], [9].) Further advances were made in [12], where among other things the Independence Theorem for Lascar strong types was proved. This is a theorem concerning the compatibility of various free extensions, and was motivated by earlier work of Hrushovski ([5]) in a certain finite-dimensional context.…”

Supersimplicity and quadratic extensions

“…Shelah's simple theories [11] were shown to be a good setting to adapt some of the ideas of geometric model theory after the results of Kim and Pillay [5]. In doing so, new ideas and methods need to be developed, because of the weakness of simplicity (or rather, strength of stability) when carrying over some of the arguments.…”