Let $r_1<r_2<..<r_s$ and $k$ be positive integers. Prove that there is $n(k; r_1,r_2,...,r_s)$ with the following property. For every colorings of ${[n]}\choose{i}$ with $r_i$ colors, $i=1,...,s$, there is a subset $K\in$${[n]}\choose{k}$ such that all $i$-sets of $K$ are monochromatic.
Hello, I have been reading about Ramsey's Theorem by my self and trying to do some exercises. Although I did some of them, I am not being able to get this. That's why it would be nice if someone can help me or give to me some hints!
Thanks for your help!