Two model theoretic proofs of Rückert’s Nullstellensatz
HTML articles powered by AMS MathViewer
- by Volker Weispfenning
- Trans. Amer. Math. Soc. 203 (1975), 331-342
- DOI: https://doi.org/10.1090/S0002-9947-1975-0369060-0
- PDF | Request permission
Abstract:
Rückert’s Nullstellensatz for germs of analytic functions and its analogue for germs of real analytic functions are proved by a combination of nonstandard analysis with a model theoretic transfer principle. It is also shown that Rückert’s Nullstellensatz is constructive essentially relative to the Weierstrass preparation theorem.References
- D. W. Dubois, A nullstellensatz for ordered fields, Ark. Mat. 8 (1969), 111–114. MR 272761, DOI 10.1007/BF02589551 G. Efroymson, Local reality, Univ. of New Mexico, Technical Report Nr. 257, 1972.
- Jean-Jacques Risler, Un théorème des zéros en géométrie analytique réelle, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A1488–A1490 (French). MR 294686
- Abraham Robinson, Germs, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 138–149. MR 0236427
- Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854
- Abraham Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland Publishing Co., Amsterdam, 1963. MR 0153570
- A. Seidenberg, Some remarks on Hilbert’s Nullstellensatz, Arch. Math. (Basel) 7 (1956), 235–240. MR 81929, DOI 10.1007/BF01900296
- Alfred Tarski, A decision method for elementary algebra and geometry, University of California Press, Berkeley-Los Angeles, Calif., 1951. 2nd ed. MR 0044472, DOI 10.1525/9780520348097
- Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0120249, DOI 10.1007/978-3-662-29244-0
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 203 (1975), 331-342
- MSC: Primary 02H25; Secondary 14A25, 26A90, 32B10
- DOI: https://doi.org/10.1090/S0002-9947-1975-0369060-0
- MathSciNet review: 0369060