Kobe Colloquium on Logic, Statistics and Informatics

以下の要領で神戸情報数理コロキウムを開催します。

【１】（日程が変更になりました） 日時：2011年9月22日（木）15:00 ～ 16:00 場所：神戸大学自然科学総合研究棟3号館4階421室（渕野グループ内プレゼンテーション室） 講演者：Florian Pelupessy（Ghent 大学） 題目：Phase transitions for unprovability

アブストラクト： The talk will be an introduction to phase transitions for unprovability: theorems with a parameter function change from provable to unprovable with a change in that parameter.

Additionally we will present a transitiona for a Ramsey-like statement and for a theorem by Maclagan on monomial ideals.

【２】 日時：2011年10月18日（火）14:00 ～ 15:00 場所：神戸大学自然科学総合研究棟3号館4階421室（渕野グループ内プレゼンテーション室） 講演者：Sam Sanders（東北大学，Ghent 大学） 題目：Reverse-engineering (Constructive) Reverse Mathematics

アブストラクト： Constructive Analysis was introduced by Erret Bishop to identify the `computational meaning' of Mathematics. In the spirit of intuitionistic mathematics, notions like `algorithm', `explicit computation' and `finite procedure' are central. The exact meaning of these vague terms was left open, to ensure the compatibility of Constructive Analysis with several traditions in Mathematics. Bishop did explicitly identity many non-algorithmic principles, thus implicitly defining `algorithm'. One of the goals of Constructive Reverse Mathematics (CRM) is to analyze the role of these non-algorithmic principles in Mathematics.

Bishop famously derided Nonstandard Analysis for its lack of computational meaning. In this talk, we introduce `$\Omega$-invariance' : a simple and elegant definition of `finite procedure' in (classical) Nonstandard Analysis. Using an intuitive interpretation, we obtain many results from CRM, thus showing that $\Omega$-invariance is quite close to Bishop's notion of `algorithm'.

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]