  H. Furstenberg introduced the notion of central set in terms of topological
dynamics and established the central set theorem. The essence of central set
theorem is that it is the simultaneous extension of van der Waerden's theorem
and Hindman's theorem. Later V. Bergelson and N. Hindman established a
connection between central sets and the algebra of Stone-cech compactification
and proved that the central sets are the member of minimal idempotent
ultrafilter of discrete semigroup. In some subsequent papers the central set
theorem has been studied more deeply and some generalizations has been
established. Those works use the techniques of Stone-Cech compactification of
discrete semigroup. In this work we will prove central set theorem via
combinatorial approach using the combinatorial characterization of central set
established by N. Hindman, A. Malkeki and D. Strauss. Though we will use the
combinatorial approach but the technique of the proof is similar to the proof
of D. De, N. Hindman, D. Strauss.
