J un 2 00 5 A partition theorem for a large dense linear order

@inproceedings{Dzamonja2008JU2,
title={J un 2 00 5 A partition theorem for a large dense linear order},
author={Mirna Dzamonja and Jean A. Larson and William J. Mitchell},
year={2008}
}

Let Qκ = (Q,≤Q) be a strongly κ-dense linear order of size κ for κ a suitable cardinal. We prove, for 2 ≤ m < ω, that there is a finite value tm such that the set [Q] m of m-tuples from Q can be divided into tm many classes, such that whenever any of these classes C is colored with < κ many colors, there is a copy Q∗ of Qκ such that [Q ∗]m ∩C is monochromatic. As a consequence we obtain that whenever we color [Qκ] m with < κ many colors, there is a copy of Qκ all m-tuples from Support by EPSRC… CONTINUE READING