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Artin Approximation via the Model Theory of Cohen-Macaulay Rings

Published online by Cambridge University Press:  31 March 2017

Hans Schoutens
Affiliation:
Wesleyan University,Middletown
Samuel R. Buss
Affiliation:
University of California, San Diego
Petr Hájek
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Pavel Pudlák
Affiliation:
Academy of Sciences of the Czech Republic, Prague
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Logic Colloquium '98 , pp. 409 - 425
Publisher: Cambridge University Press
Print publication year: 2000

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References

1. Artin, M.: Algebraic approximation of structures over complete local rings. Publ. Math. I.H.E.S. 36 (1969) 23–58Google Scholar
2. Artin, M.: On the solutions of analytic equations. Invent. Math. 5 (1968) 177–291Google Scholar
3. Bass, H.: On the ubiquity of Gorenstein rings. Math. Z. 82 (1963) 8–28Google Scholar
4. Becker, J., Denef, J., Lipshitz, L., van den Dries, L.: Ultraproducts and approximation in local rings I. Invent. Math. 51 (1979) 189–203Google Scholar
5. Bosch, S., Güntzer, U., Remmert, R.: Non-archimedean analysis. Springer-Verlag, Berlin (1984).
6. Bruns, W., Herzog, J.: Cohen-Macaulay rings. Cambridge Univ. Press, Cambridge (1993.
7. Hodges, W.: Model Theory. Cambridge Univ. Press, Cambridge (1993).
8. Jensen, C.U., Lenzing, H.: Model Theoretic Algebra. Algebra, Logic and Applications Series, Gordon and Breach Science Publishers 2, Cambridge (1989).
9. Matsumura, H.: Commutative ring theory. Cambridge University Press, Cambridge (1986).
10. Robinson, A.: Introduction to model theory and to the metamathematics of algebra. North Holland, Amsterdam (1965).
11. Schoutens, H.: Existentially Closed Models of the Theory of Artinian Local Rings. J., Symb. Logic (1998) (to appear)
12. Schoutens, H.: The Model Theory of Artinian Local Gorenstein Rings. (1998) (preprint)
13. Schoutens, H.: Bounds in cohomology. Israel J. Math. (1998) (to appear)
14. Strooker, J.: Homological questions in local algebra. LMS Lect. Note Ser. 145, Cambridge University Press (1990).

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