A proof of a partition theorem for
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 . Unlike the original proof which is (still unpublished) long and uses the language of category theory, our proof is short and uses direct combinatorial reasoning.
- 1. D.Devlin, Some partition theorems and ultrafilters on , Ph.D. thesis, Dartmouth College (1979).
- 2. J. D. Halpern and H. Läuchli, A partition theorem, Trans. Amer. Math. Soc. 124 (1966), 360–367. MR 0200172, 10.1090/S0002-9947-1966-0200172-2
- 3. Keith R. Milliken, A Ramsey theorem for trees, J. Combin. Theory Ser. A 26 (1979), no. 3, 215–237. MR 535155, 10.1016/0097-3165(79)90101-8
- D.Devlin, Some partition theorems and ultrafilters on , Ph.D. thesis, Dartmouth College (1979).
- J.D.Halpern and H.Luchli, A partition theorem, Trans. Amer. Math. Soc. 124 (1966), 360-367. MR 34:71
- K.Milliken, A Ramsey Theorem for Trees, J. Combinatorial Theory A 26 (1979), 215-237. MR 80j:05090
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 05A18
Retrieve articles in all journals with MSC (2000): 05A18
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada MS5 1A1
Keywords: Partitions of rationals
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
Article copyright: © Copyright 2002 American Mathematical Society