Exact classes and smooth approximation
Abstract:
I will introduce the notion of an exact class, a special kind of asymptotic class whose historical origins lie with the 1992 result of Chatzidakis, van den Dries and Macintyre on definable sets in finite fields. I will then introduce the notion of smooth approximation, a definition stemming from the work of Lachlan in the 1980s on $\aleph_0$-categorical structures. I will then state and sketch a proof of a new result linking the two notions. Joint work with Sylvy Anscombe (UCLan), Dugald Macpherson (Leeds) and Charles Steinhorn (Vassar).
I will introduce the notion of an exact class, a special kind of asymptotic class whose historical origins lie with the 1992 result of Chatzidakis, van den Dries and Macintyre on definable sets in finite fields. I will then introduce the notion of smooth approximation, a definition stemming from the work of Lachlan in the 1980s on $\aleph_0$-categorical structures. I will then state and sketch a proof of a new result linking the two notions. Joint work with Sylvy Anscombe (UCLan), Dugald Macpherson (Leeds) and Charles Steinhorn (Vassar).