Two remarks on Ramsey's theorem (Q1059632)

For two classical results of Ramsey theory new simple proofs are given: Theorem (Erdős, Rado): (AC) for all \(\gamma\), \(\gamma \nrightarrow (\omega)_ 2^{\omega}\). This is reduced to the fact that using AC a bipartite graph may be 2-colored. Theorem (Deuber; Něsetřil, Rödl). Let \(k,p<\omega\). For every finite graph G there exists a graph H such that \(H\to (G)_ k^{K_ p}\). This ingeniously simple proof makes use of the Graham-Rothschild theorem for n-parametersets, applied to setsystems.