Kobe Colloquium on Logic, Statistics and Informatics

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日時：2013年8月13日（火）13:20-14:50 講演者：Luz García (バルセロナ大学と神戸大学) 場所：神戸大学自然科学総合研究棟3号館4階421室（プレゼンテーション室）

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題目： Forcing Arguments in Infinite Ramsey Theory

アブストラクト： Neil Hindman proved a Ramsey-like result that was conjectured by Graham and Rotschild. Hindman's Theorem asserts that if the set of all natural numbers is divided into two classes, one of the classes contains an infinite set such that all finite sums of distinct members of the set remain in the same class. Hindman's original proof was greatly simplified by James Baumgartner.

We will present a proof of this theorem which relies on forcing arguments. The analysis of the partial order arising in the proof of Hindman's Theorem, which we denote by P_{FIN}, is our main interest.

The partial order P_{FIN} is similar both to the one due to Matet and to Mathias forcing. This prompts the question whether it is equivalent to one of them or not.

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交通：阪急六甲駅またはJR六甲道駅から神戸市バス36系統「鶴甲団地」 行きに乗車，「神大本部工学部前」停留所下車，徒歩すぐ． http://www.kobe-u.ac.jp/info/access/rokko/rokkodai-dai2.htm