We prove a version of the Ramsey theorem for partitions of (increasing) n-tuples. We derive this result from a version of König's infinity lemma for ξ-large trees. Here ξ < ε₀ and the notion of largeness is in the sense of Hardy hierarchy.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-2-2,
author = {Teresa Bigorajska and Henryk Kotlarski},
title = {Some combinatorics involving $\xi$-large sets},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {119-125},
zbl = {1010.05006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-2-2}
}
Teresa Bigorajska; Henryk Kotlarski. Some combinatorics involving ξ-large sets. Fundamenta Mathematicae, Tome 173 (2002) pp. 119-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-2-2/