A proof of a partition theorem for $[\mathbb Q]^n$
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- by Vojkan Vuksanovic PDF
- Proc. Amer. Math. Soc. 130 (2002), 2857-2864 Request permission
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 Unlike the original proof which is (still unpublished) long and uses the language of category theory, our proof is short and uses direct combinatorial reasoning.References
- D.Devlin, Some partition theorems and ultrafilters on $\omega$, Ph.D. thesis, Dartmouth College (1979).
- J. D. Halpern and H. Läuchli, A partition theorem, Trans. Amer. Math. Soc. 124 (1966), 360–367. MR 200172, DOI 10.1090/S0002-9947-1966-0200172-2
- Keith R. Milliken, A Ramsey theorem for trees, J. Combin. Theory Ser. A 26 (1979), no. 3, 215–237. MR 535155, DOI 10.1016/0097-3165(79)90101-8
Additional Information
- Vojkan Vuksanovic
- Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada MS5 1A1
- Email: voja@math.toronto.edu
- Received by editor(s): March 29, 2001
- Received by editor(s) in revised form: May 29, 2001
- Published electronically: March 25, 2002
- Communicated by: Alan Dow
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2857-2864
- MSC (2000): Primary 05A18
- DOI: https://doi.org/10.1090/S0002-9939-02-06460-2
- MathSciNet review: 1908908