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

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 24 references

A Strongly Non-Ramsey Order Type

Combinatorica • 1997
View 9 Excerpts
Highly Influenced

Universal graphs and universal functions

Richard Rado
Acta Arithmetica, • 1964
View 20 Excerpts
Highly Influenced

Infinite partitions of random graphs

J. Comb. Theory, Ser. A • 2006
View 10 Excerpts
Highly Influenced

Two Cardinal Properties of Homogeneous Graphs

J. Symb. Log. • 2002
View 11 Excerpts
Highly Influenced

Coloring Subgraphs of the Rado Graph

Combinatorica • 2006
View 1 Excerpt
Highly Influenced

A combinatorial proof of a partition relation for [Q

Vojkan Vuksanovic
Proc. Amer. Math. Soc., • 2002
View 4 Excerpts
Highly Influenced

A Ramsey Theorem for Trees

J. Comb. Theory, Ser. A • 1979
View 3 Excerpts
Highly Influenced

A Partition Theorem

James Halpern, H. LÄUCHLI
2010
View 1 Excerpt

Similar Papers

Loading similar papers…