Progression and Set Theory

In Ramsey theory, a set S of natural numbers is considered to be a large set if and only if Van der Waerden’s theorem can be generalized to assert the existence of arithmetic progressions with common difference in S. That is, S is large if and only if every finite partition of the natural numbers has a cell containing arbitrarily long arithmetic progressions having common differences in S.

IIM B, C, L, K, S.P. Jain

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