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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Two model theoretic proofs of Rückert's Nullstellensatz


Author: Volker Weispfenning
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0369060-0
Keywords: Rückert's Nullstellensatz, nonstandard germs of analytic and real analytic functions, transfer principle
Article copyright: © Copyright 1975 American Mathematical Society