Sub-Pfaffian sets and a generalization of Wilkie's theorem

• Autorzy: Hajto Z.
• Języki publikacji: EN

Abstrakty

EN

We prove an analytic generalization of A. Wilkie's well-known theorem on the model completeness of the theory of the real field with exponentiation.

Słowa kluczowe

EN

Pfaffan systems; stratifications; subanalytic sets

PL

stratyfikacja; układ Pfaffa; zbiór subanalityczny

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 2
• Strony: 181--189
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Hajto Z.

• Institut of Mathematics, University of Agriculture, Królewska 6, 30-045 Kraków, Poland

Bibliografia

• [1] A. B. Cabello Pardos, Z. Hajto, Stratifications adapted to finite families of differential 1-forms, (Pfaffian geometry - part one), Rev. Mat. Univ. Complut. Madrid, 8 (2) (1995) 269-292.
• [2] D. Cerveau, A. Lins Neto, Codimension one foliations in ℂℙn, n .≥ 3, with Kupka components, Astćrisque, 222 (1994) 93-133.
• [3] Z. Denkowska, S. Łojasiewicz, J. Stasica, Sur le théorème du complementaire pour les ensembles sous-analytiques, Bull. Acad. Pol. Sci., Sér. Math., XXVII (7-8) (1979) 537-639.
• [4] L. van den Dries, C. Miller, Geometric categories and o-minimal structures, Duke Math. J., 84 (2) (1996) 497-540.
• [5] A. M. Gabrielov, Complements of subanalytic sets and existential formulas for analytic functions, Invent. Math., 125 (1996) 1-12.
• [6] Z. Hajto, On the Gabrielov theorem for sub-Pfaffian sets, in: Real Analytic and Algebraic Geometry, eds.:F. Broglia, M. Galbiati, A. Tognoli, Walter de Gruyter (1995) 149-160.
• [7] Z. Hajto, Lemmas A and B for sub-Pfaffian sets, Bull. Pol. Ac.: Math., 47 (4) (1999) 325-336.
• [8] A. G. Hovanskii, Fewnomials and Pfaff manifolds, Proc. Internat. Congress of Mathematicians, Warsaw (1983) 549-564.
• [9] A. G. Hovanskii, Fewnomials, Transl. Math. Monogr., 88 (1991).
• [10] I. Kupka, The singularities of integrable structurally stable Pfaffian forms, Proc. Nat. Acad. Sci. U.S.A., 52 (1964) 1431-1432.
• [11] S. Łojasiewicz z, Ensembles semianalytiques, Publ. Math. IHES, Bures-sur-Yvette, 1965.
• [12] S. Łojasiewicz, Stratifications et triangulations sous-analytigues, Seminari Geometria Bologna, (1986) 83-97.
• [13] S. Łojasiewicz, M. A. Zurro, Introducción a la Geometria semi y sub-analítica, Universidad de Valladolid, 1993.
• [14] R. Moussu, C. Roche, Thdormes de finitude pour les variétés pfaffiennes, Ann. Ins. Fourier (Grenoble), 42 (1-2) (1992) 393-420.
• [15] J. Stasica, The Whitney condition for subanalytic sets, Zeszyty Nauk. U.J. Mat., 32 (1982) 211-221.
• [16] Ta Lê Loi, Analytic cell decomposition of sets definable in the structure ℝexp, Ann. Polon. Math., 59 (3) (1994) 255-266.
• [17] A. J. Wilkie, Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function, J. Amer. Math. Soc., 9 (1996) 1051-1094.
• [18] A. J. Wilkie, O-minimality, Proc. Internat. Congress of Mathematicians, Vol. I, Berlin (1998) 333-336.