Elisabeth Bouscaren : Finitely axiomatisable strongly minimal groups

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

March 28, 2006, 4 p.m.

In

SEO 427

Abstract

The existence of a finitely axiomatisable $\aleph_1$-categorical theory with non-trivial geometry is open. Hrushovski has shown that such a theory must have a locally modular geometry, and conjectured that the existence of such a theory was equivalent to the existence of a division ring finitely presented as a ring. In joint work with Thomas Blossier, we have shown that if $G$ is a finitely axiomatisable strongly minimal group, then the ring of quasi-endomorphisms of G is indeed finitely presented.