# Measurable structures, and asymptotics in finite structures

Presented by:
D Macpherson [Leeds]
Date:
Thursday 23rd June 2005 -
15:30 to 17:00
Venue:
INI Seminar Room 1
Abstract:

Work of Chatzidakis, van den Dries and Macintyre [CDM] shows that in finite fields, the sizes of definable sets (defined by a fixed formula with parameters) have a uniform asymptotic behaviour as the field and parameters vary. This enables one to associate a dimension (the natural one) and a measure to any definable set in a pseudofinite field. I and Steinhorn have investigated arbitrary classes of finite structures for which the conclusion of the [CDM] theorem holds, and the corresponding notion of (supersimple) measurable structure. In this talk I will describe examples, but will mainly discuss more recent work of Ivan Tomasic, Richard Elwes, and Mark Ryten.