皆様

名古屋大学の木原貴行です．

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名古屋ロジックセミナー http://www.math.mi.i.nagoya-u.ac.jp/~kihara/logic-seminar.html

日時：3月12日 (月) 15:30〜 場所：名古屋大学大学院情報学研究科棟 314室

講演者：Vassilios Gregoriades (トリノ大学)

題目： The Preiss Separation Theorem uniformly

アブストラクト： The typical example of a uniformity-type result in descriptive set theory is the Souslin-Kleene Theorem, which says that the separation property of the class of analytic sets can be witnessed by a recursive function in the codes. An important consequence of the latter is the extension of the result HYP = effectively bi-analytic, in all recursive Polish spaces.

In this talk we present the uniform version of a separation result by Preiss that deals with the convex analytic subsets of the Euclidean space. We show that the separation can be realized by a HYP function in the codes. Similarly to the case of the Souslin-Kleene Theorem, we conclude that every HYP convex subset of the Euclidean space can be obtained from the class of HYP compact convex sets by taking HYP increasing unions and HYP intersections.

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Takayuki Kihara Graduate School of Informatics, Nagoya University, Japan URL: http://math.mi.i.nagoya-u.ac.jp/~kihara/index-j.html Email: [email protected]