The model theory of differential fields of characteristic $p\not =0$
HTML articles powered by AMS MathViewer
- by Carol Wood PDF
- Proc. Amer. Math. Soc. 40 (1973), 577-584 Request permission
Abstract:
The theory of differential fields of characteristic $p \ne 0$ is shown to have a model companion, the theory of differentially closed fields, which is moreover the model completion of the theory of differentially perfect fields. It is also shown that the theory of differentially closed fields.is not $\omega$-stable.References
-
L. Blum, Thesis, M.I.T., Cambridge, Mass., 1968.
- Paul Eklof and Gabriel Sabbagh, Model-completions and modules, Ann. Math. Logic 2 (1970/71), no.Β 3, 251β295. MR 277372, DOI 10.1016/0003-4843(71)90016-7
- Nathan Jacobson, Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. MR 0172871, DOI 10.1007/978-1-4612-9872-4 A. Robinson, An introduction to model theory, North-Holland, Amsterdam, 1965.
- Abraham Robinson, On the concept of a differentially closed field, Bull. Res. Council Israel Sect. F 8F (1959), 113β128 (1959). MR 125016
- Gerald E. Sacks, Saturated model theory, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass., 1972. MR 0398817
- A. Seidenberg, An elimination theory for differential algebra, Univ. California Publ. Math. (N.S.) 3 (1956), 31β65. MR 82487
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 577-584
- MSC: Primary 02H15; Secondary 12H05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0329887-1
- MathSciNet review: 0329887