Zhang, Chuanlin; Yu, Kai A counting theorem on semi-algebraic set and its applications. (Chinese. English summary) Zbl 0955.14041 J. Math. Res. Expo. 20, No. 2, 266-270 (2000). Summary: In this paper, a counting theorem about the cardinality of semi-algebraic set is given by using Tarski’s principle. Basing on the principle, a method to calculate the Euler characteristic and the genus of a compact algebraic manifold is presented. MSC: 14P10 Semialgebraic sets and related spaces 03E10 Ordinal and cardinal numbers 13J30 Real algebra Keywords:cardinality of semi-algebraic set; Tarski’s principle; Euler characteristic; genus PDFBibTeX XMLCite \textit{C. Zhang} and \textit{K. Yu}, J. Math. Res. Expo. 20, No. 2, 266--270 (2000; Zbl 0955.14041)