A Short Proof of a Partition Relation for Triples

We provide a much shorter proof of the following partition theorem of P. Erdos and R. Rado: If X is an uncountable linear order into which neither 1 nor 1 embeds, then X (, 4)3 for every ordinal < + . We also provide two counterexamples to possible generalizations of this theorem, one of which answers a question of E. C. Milner and K. Prikry. MR Subject Classifications: 03E05, 04A20, 05A18, 05D10

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Albin L. Jones
• Keywords: COMBINATORICS 2000, MR Subject Classifications, Shorter Proof, Uncountable Linear Order