Model theory is a branch of mathematical logic dealing with mathematical structures (models). Model theory is traditionally divided into two parts pure and applied. Pure model theory studies abstract properties of first order theories, and derives structure theorems for their models. Originally, a good description of models was available only for so-called superstable theories, which is quite a restricted class. Nowadays, there is a great progress in extending the methods and results of pure model theory to wider and wider classes of theories (e.g. dependent, simple). There are also interesting new connections between pure model theory and descriptive set theory.
Applied model theory on the other hand studies concrete algebraic structures from a model-theoretic point of view, and uses results from pure model theory to get a better understanding of the structures in question. Applied model theory usually subdivides into algebraic and o-minimal (analytic) parts. The algebraic part deals almost exclusively with different theories of fields, which are sometimes enriched with an additional structure (as derivation or automorphism). This is the part of model theory in which the most spectacular applications have occurred for example Hrushovski’s proof of the positive characteristic version of the Mordell-Lang conjecture. O-minimality deals with theories of ordered (hence topological) fields satisfying certain tameness properties. Model theory has strong connections to other branches of mathematics as algebra, analysis and geometry and its results often have implications in these areas. Our aim is to treat these different sub-branches of model theory rather equally. Leading world specialists in each sub-field of model theory have already accepted to give lectures about newest developments in their respective fields.
All young researchers are strongly encouraged to bring a poster & participate in the Poster Sessions.