Submission date: 19 October 2009.

Abstract:

In this paper we study the model theory of classes of finite Moufang polygons. We show that each family of finite Moufang polygons forms an `asymptotic class'. As a result, since every non-principal ultraproduct of an asymptotic class is `measurable', and therefore supersimple of finite rank, we obtain examples of (infinite) supersimple Moufang polygons of finite rank. In a forthcoming paper we will show that all supersimple Moufang polygons of finite rank arise over supersimple fields, and belong to exactly those families which also have finite members.

Mathematics Subject Classification: 51E12, 03C13, 03C98

Keywords and phrases: generalized Moufang polygons, Chevalley groups, twisted groups of fixed Lie type and Lie rank, groups with a BN-pair, asymptotic classes of finite structure, measurable structures, bi-interpretability, supersimple structures of finite rank.

Full text: pdf, dvi, ps.