Geodesic
A short proof of a partion relation for triples
The electronic journal of combinatorics, Tome 7 (2000)
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We provide a much shorter proof of the following partition theorem of P. Erdős and R. Rado: If $X$ is an uncountable linear order into which neither $\omega_1$ nor $\omega_1^{*}$ embeds, then $X \to (\alpha, 4)^{3}$ for every ordinal $\alpha < \omega + \omega$. We also provide two counterexamples to possible generalizations of this theorem, one of which answers a question of E. C. Milner and K. Prikry.
DOI : 10.37236/1502
Classification : 03E02, 05D10
Mots-clés : partition relations, ordered sets 
@article{10_37236_1502,
     author = {Albin L. Jones},
     title = {A short proof of a partion relation for triples},
     journal = {The electronic journal of combinatorics},
     year = {2000},
     volume = {7},
     doi = {10.37236/1502},
     zbl = {0945.03067},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1502/}
}
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Albin L. Jones. A short proof of a partion relation for triples. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1502

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