\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Dibyendu De and Ram Krishna Paul}
%
%
\medskip
\noindent
%
%
{\bf Universally Image Partition Regularity}
%
%
\vskip 5mm
\noindent
%
%
%
%
Many of the classical results of Ramsey Theory, for example Schur's
Theorem, van der Waerden's Theorem, Finite Sums Theorem, are naturally
stated in terms of {\em image partition regularity\/} of matrices.
Many characterizations are known of image partition regularity over
${\Bbb N}$ and other subsemigroups of $({\Bbb R},+)$. In this paper we
introduce a new notion which we call {\em universally image partition
regular matrices\/}, which are in fact image partition regular over
all semigroups and everywhere. We also prove that such matrices exist
in abundance.



\bye

.