About splitting numbers
The main purpose of this paper is to present a proof of the following theorem with some expositions for working mathematicians who are not set theorists. Theorem 1. Suppose that \(\kappa\) is an uncountable regular cardinal. Then, the splitting number of \(\kappa\) is strictly larger than \(\kappa\) if and only if \(\kappa\) is a weakly compact cardinal. In August 1992, the author reported a sketch of a proof of Theorem 1, and that of Proposition 2, on a meeting at the Research Institute of Mathematical Sciences, Kyoto University. Since then, a previous version of our current paper has been circulated among some set theorists. In October 1992, J. Zapletal, who was a graduate student of the Pennsylvania State University at that time, informed us that he improved our results. Nowadays, the theory of splitting numbers at uncountable cardinals relates to various branches of set theory such as inner model theory and Shelah's pcf theory. Our current paper is the final version of the preprint with the same title, which appears in the list of references of \textit{J. Zapletal's} paper [``Splitting number at uncountable regular cardinals'', J. Symb. Log. 62, 35-42 (1997; Zbl 0874.03058)].
scientific article; zbMATH DE number 1192516