Ramsey's theorem for spaces

Author:
Joel H. Spencer

Journal:
Trans. Amer. Math. Soc. **249** (1979), 363-371

MSC:
Primary 05A99; Secondary 05C55

MathSciNet review:
525678

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Abstract: A short proof is given of the following known result. For all *k*, *r*, *t* there exists *n* so that if the *t*-spaces of an *n*-space are *r*-colored there exists a *k*-space all of whose *t*-spaces are the same color. Here *t*-space refers initially to a *t*-dimensional affine space over a fixed finite field. The result is also shown for a more general notion of *t*-space.

**[1]**R. L. Graham, K. Leeb, and B. L. Rothschild,*Ramsey’s theorem for a class of categories*, Advances in Math.**8**(1972), 417–433. MR**0306010****[2]**R. L. Graham and B. L. Rothschild,*Ramsey’s theorem for 𝑛-parameter sets*, Trans. Amer. Math. Soc.**159**(1971), 257–292. MR**0284352**, 10.1090/S0002-9947-1971-0284352-8**[3]**A. W. Hales and R. I. Jewett,*Regularity and positional games*, Trans. Amer. Math. Soc.**106**(1963), 222–229. MR**0143712**, 10.1090/S0002-9947-1963-0143712-1

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DOI:
https://doi.org/10.1090/S0002-9947-1979-0525678-7

Article copyright:
© Copyright 1979
American Mathematical Society