THE TOPOLOGICAL PIGEONHOLE PRINCIPLE FOR ORDINALS
نویسندگان
چکیده
منابع مشابه
The Topological Pigeonhole Principle for Ordinals
Given a cardinal κ and a sequence (αi )i∈κ of ordinals, we determine the least ordinal (when one exists) such that the topological partition relation
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As a story, this means that at a party with n persons, there exist two persons who know the same number of people at the party. Proof. For any graph on n vertices, the degrees are integers between 0 and n − 1. Therefore, the only way all degrees could be different is that there is exactly one vertex of each possible degree. In particular, there is a vertex v of degree 0 (with no neighbors) and ...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2016
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2015.45