The Siegel theorem on Diophantine equations
This is a largely expository paper. Siegel's theorem states that certain affine curves have only finitely many integral points over any given subring of \(\bar\mathbb{Q}\) of finite type over \(\mathbb{Z}\). This paper presents the proof of this theorem, assuming Roth's theorem, from the point of view of nonstandard analysis: cf. \textit{A. Robinson} and \textit{P. Roquette} [J. Number Theory 7, 121-176 (1975; Zbl 0299.12107)]. The exposition is elementary except that, as the author notes, increasing amounts of algebraic geometry are needed as the exposition progresses. The paper also assumes a knowledge of nonstandard analysis.
scientific article; zbMATH DE number 8528