David Evans: The Hrushovski constructions in combinatorics and model theory.
The main focus of these talks is on the Hrushovski amalgamation constructions. These date back to the late 1980's and are very important in model theory. At the time, they provided counterexamples to several appealing conjectures in model theory and there continue to be new applications in model theory.
In these talks we will look at the constructions from the point of view of structural Ramsey theory and topological dynamics and will see that, here also, they give rise to new phenomena. In particular, they give us examples to show that there is a countable omega-categorical structure with no precompact Ramsey expansion.
The talks will give a self-contained exposition of the Hrushovski constructions (similar to the notes ) and I will explain the proof of the above result.
The original parts of the talks are from on-going joint work with J. Hubička and J. Nešetřil.
- David Evans, "Homogeneous structures, omega-categoricity and amalgamation constructions", talks given at the Hausdorff Institute for Mathematics, Bonn, September 2013. Available at http://wwwf.imperial.ac.uk/~dmevans/Bonn2013_DE.pdf