Complements of subanalytic sets and existential formulas for analytic functions
The author is the same person who started, even before Hironaka, the theory of subanalytic sets in 1968 [the author, Funct. Anal. Appl. 2, 282-291 (1968); translation from Funkts. Anal. Prilozh. 2, No. 4, 18-30 (1968; Zbl 0179.08503)]. In the cited paper he proved, among other things, the essential result: the complement of a subanalytic set in \(\mathbb{R}^n\) is subanalytic. Now he proves the same result for the subanalytic sets described by a subalgebra of analytic functions, closed under differentiation. The translation into the logic is given, too. Needless to say, such a result is not easy to obtain and the author uses the newest developments (like \textit{A. G. Khovanskij} [`Fewnomials' (1991; Zbl 0728.12002)], for example). The paper is short and well written.
scientific article; zbMATH DE number 885518