Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A proof of a partition theorem for $[\mathbb Q]^n$

Author(s): Vojkan Vuksanovic
Journal: Proc. Amer. Math. Soc. 130 (2002), 2857-2864.
MSC (2000): Primary 05A18
Posted: March 25, 2002
MathSciNet review: 1908908
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Abstract | References | Similar articles | Additional information

Abstract: In this note we give a proof of Devlin's theorem via Milliken's theorem about weakly embedded subtrees of the complete binary tree $2^{<\mathbb N }$ . Unlike the original proof which is (still unpublished) long and uses the language of category theory, our proof is short and uses direct combinatorial reasoning.

References:

1.: D.Devlin, Some partition theorems and ultrafilters on $\omega$ , Ph.D. thesis, Dartmouth College (1979).
2.: J.D.Halpern and H.L $\ddot a$ uchli, A partition theorem, Trans. Amer. Math. Soc. 124 (1966), 360-367. MR 34:71
3.: K.Milliken, A Ramsey Theorem for Trees, J. Combinatorial Theory A 26 (1979), 215-237. MR 80j:05090

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