Ramsey Theory and Countable Ordinals
 发布时间： 2018-03-24     22:31   【返回上一页】 发布人：William Weiss

We write $\gamma \to (\alpha)^2_{l,k}$ provided that whenever the pairs of elements of the ordinal $$\gamma$$ are coloured with $$l$$ colours there is a subset $$C$$ of the original $$l$$ colours of size only $$k$$ and a subset $$H \subset \gamma$$ such that:
(1)  $$H$$ is homeomorphic to the ordinal $$\alpha$$ with the usual order topology,
(2)  any pair from $$H$$ is coloured by one of the colours from $$C$$.