Logic seminar

Tuesday, January 22, 2013 11:00 am - 11:00 am EST (GMT -05:00)

Pantelis Eleftheriou, Department of Pure Mathematics, University of Waterloo

Groups definable in o-minimal structures

Let M be an ordered vector space over an ordered division ring D. A subset X of Mn is called “semilinear” if it is a boolean combination of sets defined by linear equations and inequalities with coefficients from D. A ”semilinear group” is a group whose domain and the graph of its multiplication are semilinear sets. We prove that every semilinear group is semilinearly isomorphic to a quotient by a lattice, exemplifying its strong connection to a real Lie group. This study belongs to the general program of studying groups definable in o-minimal structures.