Dugald Macpherson (University of Leeds)

Around stability theory (Part 2)

• Speaker's homepage

Model-theoretic stability theory was developed in the 1970s, with Shelah in a lead role, as providing a notion of 'tameness' for first order theories. In particular, uncountably categorical theories are stable, and on the other hand a complete unstable theory over a countable language has $2^\kappa$ nonisomorphic models of size $\kappa$ for any uncountable cardinality $\kappa$. Stability can be characterised in many different ways, and stability provides a powerful notion of independence between subsets of a model.

I will give a very informal overview of stability theory, and of some of the generalisations of stability which have been developed more recently (in particular simplicity, and NIP).