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A generalization of the Tarski-Seidenberg theorem, and some nondefinability results
Author(s):
Lou
van den Dries
Journal:
Bull. Amer. Math. Soc.
15
(1986),
189-193.
MSC (1985):
Primary 03E47
MathSciNet review:
854552
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Additional information
References:
- [Ga] A. Gabrielov, Projections of semi-analytic sets, Functional Anal. Appl. 2 (1968), 282-291. (Russian) MR 245831
- [Gi] B. Gieseke, Simpliziale Zerlegung abzählbarer analytische Räume, Math. Z. 83 (1964), 177-213. MR 159346
- [Ha] R. Hardt, Semi-algebraic local triviality in semi-algebraic mappings, Amer. J. Math. 102 (1980), 291-302. MR 564475
- [Hi] H. Hironaka, Triangulation of algebraic sets, Algebraic Geometry, Arcata 1974, Proc. Sympos. Pure Math., vol. 29, Amer. Math. Soc., Providence, R. I., 1975, pp. 165-186. MR 374131
- [Ho] A. Hovanskii, Fewnomials and Pfaff manifolds, Proc. ICM, Warsaw, 1983, pp. 549-564. MR 804711
- [K-P-S] J. Knight, A. Pillay, and C. Steinhorn, Definable sets in ordered structures. II, Trans. Amer. Math. Soc. 295 (1986), 593-605. MR 833698
- [L1] S. Lojasiewicz, Ensembles semi-analytiques, mimeographed notes, Inst. Hautes Études Sci., 1965.
- [L2] S. Lojasiewicz, Triangulation of semi-analytic sets, Ann. Sci. École Norm. Sup. Pisa (3) 18 (1964), 449-474. MR 173265
- [P-S] A. Pillay and C. Steinhorn, Definable sets in ordered structures. I, Trans. Amer. Math. Soc. 295 (1986), 565-592. MR 833697
- [T] A. Tarski, A decision method for elementary algebra and geometry, (2nd ed. revised), Rand Corporation monograph, Berkeley and Los Angeles, 1951. MR 44472
- [VdD1] L. van den Dries, Analytic Hardy fields and exponential curves in the real plane, Amer. J. Math. 106 (1984), 149-167. MR 729758
- [VdD2] L. van den Dries, Remarks on Tarski's problem concerning (R, +, ·, exp), Logic Colloquium, 1982, pp. 97-121, (G. Lolli, G. Longo and A. Marcja, eds.), North-Holland, 1984. MR 762106
- [VdD3] L. van den Dries, Tarski's problem and Pfaffian functions, Proc. Logic Colloquium, 1984 (to appear).
- [VdD4] L. van den Dries, lectures at University of Konstanz.
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Additional Information:
DOI:
10.1090/S0273-0979-1986-15468-6
PII:
S 0273-0979(1986)15468-6
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