Abstract
In this paper we present a Ramsey theorem for certain categories which is sufficiently general to include as special cases the finite vector space analog to Ramsey’s theorem (conjectured by Gian-Carlo Rota), the Ramsey theorem for n-parameter sets [21, as well as Ramsey’s theorem itself [4, 61. The Ramsey theorem for finite affine spaces is obtained here simultaneously with that for vector spaces. That these two are equivalent was already known [5, II, and the arguments previously used to show that the affine theorem implies the projective theorem are also special cases of the results of this paper.
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References
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© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC
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Graham, R.L., Leeb, K., Rothschild, B.L. (2009). Ramsey’s Theorem for a Class of Categories. In: Gessel, I., Rota, GC. (eds) Classic Papers in Combinatorics. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4842-8_33
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DOI: https://doi.org/10.1007/978-0-8176-4842-8_33
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