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II. - Model Theory of Differential Fields

Published online by Cambridge University Press:  24 March 2017

David Marker ,
Margit Messmer  and
Anand Pillay
By
David Marker
David Marker
Affiliation:
University of Illinois, Chicago
Margit Messmer
Affiliation:
University of Illinois, Urbana-Champaign
Anand Pillay
Affiliation:
University of Illinois, Urbana-Champaign
David Marker
Affiliation:
University of Illinois, Chicago
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Model Theory of Fields , pp. 38 - 113
Publisher: Cambridge University Press
Print publication year: 2017

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References

Baldwin, J., Fundamentals of Stability Theory, Springer Verlag, 1988.
Hirsh, M. and Smale, S., Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, 1974.
Buiiim, A., Differential Algebra and Diophantine Geometry, Hermann, 1994.
Kaplansky, I., Differential Algebra, Hermann, 1957.
Kolchin, E., Differential Algerbra and Algebraic Groups, Academic Press, 1973.
Lang, S., Algebra, Addison Wesley, 1971.
Lang, S., Introduction to Algebraic Geometry, Interscience, 1959.
Lascar, D., Stability in Model Theory, Longman Scientific & Technical, 1987.
Magid, A., Lectures on Differential Galois Theory, American Mathematical Society, 1994.
Poizat, B., Cours de Theone des Modeles, Nur al-Mantiq wal-Ma'rifah, 1987.
Poizat, B., Groupes Stables, Nur al-Mantiq wal-Ma'rifah, 1985.
Ritt, J., Differential Algebra, Dover, 1950.
Sacks, G., Saturated Model Theory, Benjamin, 1972.
Berline, C. and Lascar, D., “Superstable groups”, Annals pure and applied logic, vol 30, 1986.Google Scholar
“Differentially closed fields: a model theoretic tour”, in Contributions to Algebra, ed. Bass, H., Cassidy, P. and Kovacic, J., Academic Press 1977.
Brestovski, M., “Algebraic independence of solutions of differential equations of the second order”, Pacific J. Math, vol 140, 1989.Google Scholar
Cherlin, G. and Shelah, S., “Superstable fields and groups”, Annals Math. Logic vol 18, 1980.Google Scholar
Gramain, F., “Non-minimalite de la cloture differentielle I: la prevue de S. Shelah”, Theories Stables, Paris Seminar Notes 1980–83.Google Scholar
Gramain, F., “Non-minimalite de la cloture differentielle II: lapreuve de M. Rosenlicht”, Theories Stables, Paris Seminar Notes 1980–83.
Hrushovski, E. and Sokolovic, Z., “Minimal subsets of differentially closed fields”, Trans. AMS, to appear.
Kolchin, E., “Existence theorems connected with the Picard-Vessiot theory of homogeneous linear ordinary differential equations”, Bulletin AMS vol. 54, 1948.Google Scholar
Kolchin, E., “Galois Theory of Differential Fields”, Amer. J. Math vol 75, 1953.Google Scholar
Kolchin, E., “Constrained extensions of differential fields”, Advances in Math, vol 12, 1974.Google Scholar
Kolchin, E., “Algebraic matrix groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations” Annals of Math vol 49, 1948.Google Scholar
Kolchin, E., “On the Galois Theory of Differential Fields”, Amer. J. Math vol 77, 1955.Google Scholar
Kolchin, E., “Abelian extensions of differential fields”, Amer. J. Math, vol 82, 1960.Google Scholar
Lascar, D., “Les corps differentiellement clos denombrables”, Theories Stables, Paris Seminar Notes 1980–83.
Lascar, D., “Relation entre le rang U et le poids”, Fundamenta Math. vol 121 (1984).Google Scholar
Macintyre, A., McKenna, K. and van den Dries, L., “Elimination of quantifiers in algebraic structures”, Advances in Math vol 47, 1983.Google Scholar
Marker, D., “Introduction to the model theory of fields”, this volume.
Michaux, C., “Sur l'élimination des quantificateurs dans les anneaux différentiels”, Comptes Rendus 47, 1983.Google Scholar
Pillay, A., “Differential algebraic groups and the number of countable differentially closed fields”, this volume.
Pillay, A. and Sokolović, Ž., “Superstable differential fields”, JSL 57, 1992.Google Scholar
Poizat, B., “Deux remarques à propos de la propriete de recouvrement fini”, Journal of Symbolic Logic, vol 49, 1984.Google Scholar
Poizat, B., “Rangs des types dan les corps differentiels”, Théories Stables, Paris Seminar Notes 1977/78.Google Scholar
Poizat, B., “Une theorie de Galois imaginaire”, Journal of Symbolic Logic vol 48, 1983.Google Scholar
Poizat, B., “C'est beau et chaud”, Théories Stables, Paris Seminar Notes 1980–83.
Rosenlicht, M., “The non-minimality of differential closure”, Pacific J. Math, vol 52, 1974.Google Scholar
Rosenlicht, M., “On Lioulville's theory of elementary functions”, Pacific J. Math, vol 65, 1976.Google Scholar
Rosenlicht, M., “A note on derivations and differentials on algebraic groups”, Portugal Math vol 16, 1957.Google Scholar
Seidenberg, A., “Abstract differential algebra and the analytic case”, Proc. AMS vol. 9, 1958.Google Scholar
Seidenberg, A., “Abstract differential algebra and the analytic case IP”, Proc. AMS vol. 23, 1969.Google Scholar
Seidenberg, A., “Some basic theorems in differential algebra (characteristic p, arbitrary)”, Trans. AMS vol. 73, 1952.Google Scholar
Shelah, S., “Differentially closed fields”, Israel J. Mathematics vol 16, 1973.Google Scholar
Wood, C., “The model theory of differential fields revisited”, Israel Journal of Mathematics, vol 25, 1976.Google Scholar

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