Kobe Colloquium on Logic, Statistics and Informatics
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日時：2013年2月6日（水）15:10-16:40 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） 講演者：Florian Pelupessy (Ghent)
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題目：Connecting the provable with the unprovable
アブストラクト： Since Gödels famous incompleteness theorems it is well known that there exist theorems which are not provable in Peano Arithmetic. In the last decades of the last century many mathematically interesting examples of such unprovable statements emerged, for example: the Paris-Harrington theorem, the Kanamori-McAloon theorem, Kruskal's tree theorem, Hydra battles and Goodstein sequences. In these theorems it is possible to insert a parameter function, where the resulting theorem variant with constant parameter is provable, but the variant with as parameter the identity function is unprovable. An obvious question in these cases is at which threshold between those functions (ordered by eventual domination) the resulting theorem changes from provable to unprovable: the phase transition for provability of the theorem. We study these phase transitions with the goal of better understanding unprovability.
We will be examining the transition results for three Ramsey theorem variants: Friedman's adjacent Ramsey theorem, the Paris-Harrington theorem and the Kanamori-McAloon theorem. For these theorems it is possible to show a deep connection between lower/upper bound estimates for the variants with constant parameter values and the threshold values for the parametrised theorems. This shows an influence of mathematics which is provable at a level slightly stronger than exponential function arithmetic on provabiltiy at the level of Peano Arithmetic.
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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
連絡先：菊池誠 [email protected]