We prove that even the prime, differentially closed field of characteristic zero, is not minimal; that over every differential radical field of characteristicp, there is a closed prime one, and that the theory of closed differential radical fields is stable.
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- 1.L. Blum,Generalized Algebraic Structures: Model Theoretic Approach, Ph. D. thesis, M. I. T., 1968.Google Scholar
- 2a.E. R. Kolchin,Constrained extension of differential fields (to appear).Google Scholar
- 4.J. F. Ritt,Differential algebra, Amer. Math. Soc. Colloquium Publ.33 (1950).Google Scholar
- 5a.M. Rosenlict,The non-minimality of the differential closure, Pacific J. Math. (to appear).Google Scholar
- 8.C. L. Siegel,Transcendental numbers, Annals of Math. Studies,16 Princeton Univ. Press, 1949.Google Scholar
- 9.S. Shelah,Differentially closed fields, Notices Amer. Math. Soc.20 (1973), A-444.Google Scholar
- 14.C. Wood,Prime model extensions of differential fields, characteristic p≠0 Notices Amer. Math. Soc.20 (1973), p. A-445.Google Scholar
- 15.C. Wood,Prime model extensions for differential fields of characteristic p≠0 (to appear).Google Scholar