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About: Ramsey class     Goto   Sponge   NotDistinct   Permalink

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In the area of mathematics known as Ramsey theory, a Ramsey class is one which satisfies a generalization of Ramsey's theorem. Suppose , and are structures and is a positive integer. We denote by the set of all subobjects of which are isomorphic to . We further denote by the property that for all partitions of there exists a and an such that . Ramsey's theorem is equivalent to the statement that the class of all finite sets is a Ramsey class.