Nonnegative solvability of linear equations in ordered Abelian groups 
       Philip Scowcroft

Abstract:

   Over an ordered field, the class of solution sets of finite systems of
   homogeneous weak linear inequalities is closed under projection, and this
   fact yields a simple proof of Farkas' theorem characterizing the
   nonnegative solvability of systems of linear equations.  If one generalizes
   the notion of inequality to that of congruence inequality--which combines
   an inequality with a congruence in a special way--then one may exploit
   techniques from model theory to show that over any Riesz group, the class
   of solution sets of finite systems of congruence inequalities is closed
   under projection.  Thus many partially ordered rings other than fields obey
   versions of Farkas' theorem, and this talk will describe such results for
   dense subrings of the reals and for the integers.