[logic-ml] Nagoya Set Theory Seminar

[吉信 康夫]

名古屋集合論セミナーのご案内：

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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名古屋大学大学院情報科学研究科
吉信康夫