Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-5cf477f64f-rdph2 Total loading time: 0 Render date: 2025-04-03T19:23:20.365Z Has data issue: false hasContentIssue false

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
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Model Theory of Fields , pp. 38 - 113
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×