Oberseminar "Mathematische Logik" - Silke Meißner

Zilber showed the following for strongly minimal first-order theories T, being theories in which formulae can't separate two infinite sets in any of its models: if T satisfies a certain notion of non-linearity, namely 1-ampleness, then a weak analogue of a projective plane, called a pseudo-plane, is interpretable in T. I will explain relevant model-theoretic notions for this topic and show a way in which this result can be generalised to 2-ample theories. Such 2-ample theories are always 1-ample, but their models have some more structure. We will call the corresponding interpretable objects pseudo-buildings, where the notion of a building was originally introduced by Tits in order to study algebraic groups. This is joint work with Katrin Tent.