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- W2088584973 abstract "Ramsey's Theorem states that for a sufficiently large set S , and for any splitting of the k -element subsets of S into r classes, there is a subset T [unk] S , [unk] T [unk] = l , such that all k -element subsets of T are in the same class. This paper establishes a theorem for certain categories that generalizes Ramsey's Theorem. In particular, it is strong enough to establish G-C. Rota's conjecture that the vector space analogue to Ramsey's Theorem is true. It also implies the Ramsey theorem for n -parameter sets, which has as corollaries, among others, the theorem of van der Waerden on arithmetic progressions and several results of R. Rado on regularity in systems of linear equations." @default.
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- W2088584973 date "1972-01-01" @default.
- W2088584973 modified "2023-09-27" @default.
- W2088584973 title "Ramsey's Theorem for a Class of Categories" @default.
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- W2088584973 doi "https://doi.org/10.1073/pnas.69.1.119" @default.
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