[logic-ml] Nagoya Set Theory Seminar

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日時：2016年7月15日(金) 午後3時30分より 場所：名古屋大学大学院情報科学研究科2階206号室

講演者：渕野昌(神戸大学) 題目：Pre-Hilbert spaces without orthonormal bases 概要：Halmos proved in 1970's that there are pre-Hilbert spaces without orthonormal bases. His example of such pre-Hilbert space was so that its dimension (size of maximal orthonormal system in the space) is strictly less than the density of the space. We show that there are also pre-Hilbert spaces X without orthonormal bases such that dim(X)=d(X). We also show that Shelah Singular Compactness Theorem holds for non-existence of orthonormal bases holds and a natural reflection statement of non-existence of orthonormal bases is equivalent to the Fodor-type Reflection Principle.

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