Andradas Heranz, CarlosDíaz-Cano Ocaña, Antonio2023-06-202023-06-202004Andradas, C., Br¨ocker, L., Ruiz, J.: Constructible sets in real geometry. Ergeb. Math. Vol. 33, Springer-Verlag, 1996 Andradas, C., Ruiz, J.: On local uniformization of orderings. AMS Contemp. Math. 155, 19–46 (1994) Becker, E.: On the real spectrum of a ring and its applications to semialgebraic geometry. Bull. Amer. Math. Soc. (N.S.) 15, 19–60 (1986) Bochnak, J., Coste, M., Roy, M.-F.: Real algebraic geometry. Ergeb. Math. Vol. 36, Springer-Verlag, 1998 Br¨ocker, L.: On basic semialgebraic sets. Expo. Math. 9, 289–334 (1991) D´ıaz-Cano, A., Andradas, C.: Stability index of closed semianalytic set germs. Math. Z. 229, 743–751 (1998) D´ıaz-Cano, A.: The t-invariant of analytic set germs of dimension 2. J. Pure Appl. Algebra 160, 157–168 (2001) Guaraldo, F.,Macr`ı, P., Tancredi, A.: Topics on Real analytic spaces.Vieweg:Advanced Lectures in Mathematics, 1986 Lam, T.Y.: An introduction to real algebra. Rocky Mountain J. Math. 14, 767–814 (1984) Matsumura, H.: Commutative algebra. Math. Lecture Note Series 56,Benjamin, 1980 Narasimhan, R.: Introduction to the theory of analytic spaces. Springer-Verlag, 1966 Ruiz, J.: The basic theory of power series. Vieweg: Advanced Lectures in Mathematics, 19930025-587410.1007/s00209-004-0650-3https://hdl.handle.net/20.500.14352/49812We show that the closed stability index of an excellent henselian local ring of real dimension d>2 with real closed residue field is (s) over bar (A) = 1/2d(d+1). When d=2 it is shown that the value of can be either 2 or 3 and give characterizations of each of these values in terms of the relation of A with its normalization and in terms of the real spectrum of A.engjournal articlehttp://www.springerlink.com/content/ne8894wgrj7qgc00/http://www.springerlink.com/restricted access512.7Geometria algebraica1201.01 Geometría Algebraica