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{\bf Dibyendu De and Ram Krishna Paul}
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{\bf Universally Image Partition Regularity}
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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.



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