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THE TOPOLOGICAL PIGEONHOLE PRINCIPLE FOR ORDINALS

Published online by Cambridge University Press:  29 June 2016

JACOB HILTON
JACOB HILTON*
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF LEEDS LEEDS LS2 9JT, UKE-mail: mmjhh@leeds.ac.uk
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Abstract

Given a cardinal κ and a sequence ${\left( {{\alpha _i}} \right)_{i \in \kappa }}$ of ordinals, we determine the least ordinal β (when one exists) such that the topological partition relation

$$\beta \to \left( {top\,{\alpha _i}} \right)_{i \in \kappa }^1$$
holds, including an independence result for one class of cases. Here the prefix “top” means that the homogeneous set must be of the correct homeomorphism class rather than the correct order type. The answer is linked to the nontopological pigeonhole principle of Milner and Rado.

Keywords

03E02pigeonhole principlepartition relationordinal topology
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016 , pp. 662 - 686
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

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