Ramsey Class

(Ramsey Theory)

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Ramsey Theory
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What is Ramsey class?

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 . Suppose is a class of structures closed under isomorphism and substructures. We say the class has the A-Ramsey property if for ever positive integer and for every there is a such that holds. If has the -Ramsey property for all then we say is a Ramsey class. Ramsey's theorem is equivalent to the statement that the class of all finite sets is a Ramsey class.

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