Multidimensional asymptotic classes and generalised measurable structures

Date

Jun 29, 2017

Time

1:15 PM - 2:15 PM

Speaker

Sylvy Anscombe

Affiliation

U of Central Lancashire, Preston, UK

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. M. Bodirsky / Prof. Dr. A. Thom

Description

Macpherson and Steinhorn introduced `1-dimensional asymptotic classes' of finite structures, which are those classes that satisfy an asymptotic counting condition on definable sets, which is modelled on Chatzidakis, van-den-Dries, and Macintyre's work on finite fields. This notion gives insights into the model theory of such classes: for example their infinite ultraproducts are supersimple of finite rank. In this talk I will introduce `multidimensional asymptotic classes', which broadens the original notion to allow more exotic examples, such as finite-dimensional vectors spaces over finite fields, equipped with a bilinear form. I will also define the notion of `generalised measurable structures', which are infinite structures satisfying an analogous condition on definable sets. I will show that free homogeneous structures are generalised measurable; and that certain homogeneous structures are not elementarily equivalent to ultraproducts of classes satisfying an *exact* version of the asymptotic condition. This is joint work with Dugald Macpherson, Charles Steinhorn, and Daniel Wolf.

Links

• Seminar Algebra, Geometrie und Kombinatorik

Last modified: Jun 23, 2017, 12:16:26 PM