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Measurable structures, and asymptotics in finite structures

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

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.

University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons