Rigid subanalytic sets
Compositio Mathematica, Tome 94 (1994) no. 3, pp. 269-295. 
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     author = {Schoutens, Hans},
     title = {Rigid subanalytic sets},
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     pages = {269--295},
     publisher = {Kluwer Academic Publishers},
     volume = {94},
     number = {3},
     year = {1994},
     mrnumber = {1310860},
     zbl = {0867.32012},
     language = {en},
     url = {http://www.numdam.org/item/CM_1994__94_3_269_0/}
}
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Schoutens, Hans. Rigid subanalytic sets. Compositio Mathematica, Tome 94 (1994) no. 3, pp. 269-295. http://www.numdam.org/item/CM_1994__94_3_269_0/

[Ba] G. Bachman, Introduction to p-adic numbers and valuation theory, New York, 1964. | MR | Zbl

[BGR] S. Bosch, U. Güntzer and R. Remmert, Non-archimedean Analysis, Springer-Verlag, Berlin, 1984. | MR | Zbl

[BM] E. Bierstone and P.D. Milman, Semianalytic and subanalytic sets, Publ. Math. I.H.E.S. 67 (1988), 5-42. | Numdam | MR | Zbl

[Bo] S. Bosch, A rigid analytic version of M. Artin's theorem on analytic equations, Math. Ann. 255 (1981), 395-404. | MR | Zbl

[DvdD] J. Denef and L. van den Dries, p-adic and real subanalytic sets, Ann. Math. 128 (1988), 79-138. | MR | Zbl

[FvdP] J. Fresnel and M. Van Der Put, Géométrie Analytique Rigide et Applications, Birkhäuser, Boston, 1981. | MR | Zbl

[Ga1] A.M. Gabrielov, Projections of semianalytic sets, Functional Anal. Appl. 2 (1968), 282-291. | MR | Zbl

[Ga2] A.M. Gabrielov, Formal relations between analytic functions, Math. USSR Izvestija 7 (1973), 1056-1088. | MR | Zbl

[Hi1] H. Hironaka, Introduction to Real-analytic Sets and Real-analytic Maps, Instituto Mathematico L. Tonelli, Pisa, 1973. | MR

[Hi2] H. Hironaka, Subanalytic sets, Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo, 1973, pp. 453-493. | MR | Zbl

[Ko] N. Koblitz, p-adic Numbers, p-adic Analysis and Zeta-functions, Springer-Verlag, New York, 1977. | MR | Zbl

[Lip] L. Lipshitz, Rigid subanalytic sets, Amer. J. Math. 115 (1993), 77-108. | MR | Zbl

[LR] L. Lipshitz and Z. Robinson, Rigid subanalytic subsets of the line and the plane (1992), 208-220 (to appear). | MR | Zbl

[Łoj1] S. Lojasiewicz, Sur la sémi analycité des images inverses par l'application tangente, Bull. Ac. Polon. Sci. 27 (1979), 525-527. | Zbl

[Łoj2] S. Lojasiewicz, Ensembles sémi-analytiques, IHES, Bures-sur-Yvette, 1965.

[Rob] A. Robinson, Complete Theories, North Holland, Amsterdam, 1966. | MR | Zbl

[Sch1] H. Schoutens, Approximation and Subanalytic Sets over a Complete Valuation Ring, Ph.D. Thesis, Leuven, 1991.

[Sch2] H. Schoutens, Uniformization of rigid subanalytic sets, Comp. Math. (1994) (to appear). | Numdam | MR | Zbl

[Sch3] H. Schoutens, Rigid subanalytic sets in the plane, J. Algebra (1993) (to appear). | MR | Zbl

[vdD] L. Van Den Dries, A specialization theorem for p-adic power series converging on the closed unit disc, J. Algebra 73(2) (1981), 613-623. | MR | Zbl

[Wei] W. Weispfenning, Quantifier elimination and decision procedures for valued fields, Models and Sets, Lect. Notes in Math., vol. 1103, Springer-Verlag, 1984, pp. 419-472. | MR | Zbl