Boolean valued analysis and type I \(AW^*\)-algebras
This note is in answer to the question raised by \textit{I. Kaplansky} [Ann. Math., II. Ser. 56, 460-472 (1952; Zbl 0047.357)] whether there is a unique cardinal number attached to a homogeneous \(AW^*\)-algebra of type I. The answer is negative as initially conjectured by him [Am. J. Math. 75, 839-858 (1953; Zbl 0051.091)]. The detailed proof of the result will be published by the author in a latter paper. The method is by way of Boolean valued analysis as developed by Takeuti and Ozawa recently.
scientific article; zbMATH DE number 3929723