On Tao's “finitary” infinite pigeonhole principle
نویسندگان
چکیده
منابع مشابه
On Tao's "finitary" infinite pigeonhole principle
In 2007, Terence Tao wrote on his blog an essay about soft analysis, hard analysis and the finitization of soft analysis statements into hard analysis statements. One of his main examples was a quasi-finitization of the infinite pigeonhole principle IPP, arriving at the “finitary” infinite pigeonhole principle FIPP1. That turned out to not be the proper formulation and so we proposed an alterna...
متن کاملExploring the Computational Content of the Infinite Pigeonhole Principle
The use of classical logic for some combinatorial proofs, as it is the case with Ramsey’s theorem, can be localized in the Infinite Pigeonhole (IPH) principle, stating that any infinite sequence which is finitely colored has an infinite monochromatic subsequence. Since in general there is no computable functional producing such an infinite subsequence, we consider a Π2-corollary, proving the cl...
متن کاملThe Pigeonhole Principle
Theorem 1.1. If n + 1 objects are put into n boxes, then at least one box contains two or more objects. Proof. Trivial. Example 1.1. Among 13 people there are two who have their birthdays in the same month. Example 1.2. There are n married couples. How many of the 2n people must be selected in order to guarantee that one has selected a married couple? Other principles related to the pigeonhole ...
متن کاملThe 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
متن کاملPigeonhole Principle and the Probabilistic Method
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2010
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1264433926