Partitioning Pairs of Uncountable Sets

Masahiro Shioya

Let κ be a regular cardinal and λ a cardinal greater than κ. Using the method of minimal walks, Todorčević gave a coloring of the pairs of x ⊂ y from [λ]^{κ} with λ colors such that every cofinal subset of [λ]^{κ} should contain a pair for each color. We will show how to push up the number of colors to λ^{+} in case κ^{cfλ} = κ.

Address: Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571 Japan

E-mail: shioyamath.tsukuba.ac.jp