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arXiv · 1410.2520

The topological pigeonhole principle for ordinals

Jacob Hilton
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Abstract

Given a cardinal $κ$ and a sequence $\left(α_i\right)_{i\inκ}$ of ordinals, we determine the least ordinal $β$ (when one exists) such that the topological partition relation \[β\rightarrow\left(top\,α_i\right)^1_{i\inκ}\] holds, including an independence result for one class of cases. Here the prefix "$top$" means that the homogeneous set must have the correct topology rather than the correct order type. The answer is linked to the non-topological pigeonhole principle of Milner and Rado.

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BibTeXRIS

Jacob Hilton. 2016-07-12. The topological pigeonhole principle for ordinals. https://doi.org/10.1017/jsl.2015.45

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