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Topological differential fields and dimension functions

Published online by Cambridge University Press:  12 March 2014

Nicolas Guzy  and
Françoise Point
Nicolas Guzy
Affiliation:
Institut de Mathématique, Université de Mons, Le Pentagone, 20, Place du Parc, B-7000 Mons, Belgium, E-mail: [email protected]
Françoise Point
Affiliation:
Institut de Mathématique, Université de Mons, Le Pentagone, 20, Place du Parc, B-7000 Mons, Belgium, E-mail: E-mail: [email protected]
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Abstract

We construct a fibered dimension function in some topological differential fields.

Keywords

Topological fieldsderivationdimension
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 4 , December 2012 , pp. 1147 - 1164
Copyright
Copyright © Association for Symbolic Logic 2012

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References

REFERENCES

[1]Brihaye, T., Michaux, C., and Riviére, C., Cell decomposition and dimension function in the theory of closed ordered differential fields, Annals of Pure and Applied Logic, vol. 159 (2009), no. 1–2, pp. 111–128.CrossRefGoogle Scholar
[2]Chang, C.C. and Keisler, H.J., Model theory, third ed., Studies in Logic and the Foundations of Mathematics, vol. 73, North Holland, 1990.Google Scholar
[3]Delon, F., Quelques propriétés des corps values en théorie des modéles, Ph.D. thesis, Université de Paris 7, 1982.Google Scholar
[4]Ealy, C. and Onshuus, A., Characterizing rosy theories, this Journal, vol. 72 (2007), no. 3, pp. 919–940.Google Scholar
[5]Guzy, N., 0-D-valued fields, this Journal, vol. 71 (2006), pp. 639–660.Google Scholar
[6]Guzy, N. and Point, F., Topological differential fields, Annals of Pure and Applied Logic, vol. 161 (2010), no. 4, pp. 570–598.CrossRefGoogle Scholar
[7]Hrushovski, E. and Scanlon, T., Lascar and Morley ranks differ in differentially closed fields, this Journal, vol. 64 (1999), no. 3, pp. 1280–1284.Google Scholar
[8]Jacobson, N., Basic algebra 2, W.H. Freeman and Company, San Francisco, 1980.Google Scholar
[9]Kirby, J., Exponential algebraicity in exponential fields, Bulletin of the London Mathematical Society, vol. 42 (2010), no. 5, pp. 879–890.CrossRefGoogle Scholar
[10]Kolchin, E.R., Differential algebra and algebraic groups, Pure and Applied Mathematics, vol. 54, Academic Press, New-York, London, 1973.Google Scholar
[11]Macintyre, A., Exponential algebra, Logic and algebra (Pontignano, 1994), Lecture Notes in Pure and Applied Mathematics, vol. 180, Dekker, New York, 1996, pp. 191–210.Google Scholar
[12]Marczewski, E., Independence and homomorphisms in abstract algebras, Fundamenta Mathematicae, vol. 50 (1961/1962), pp. 45–61.CrossRefGoogle Scholar
[13]Marker, D., Model theory: an introduction, Graduate Texts in Mathematics, vol. 217, Springer, 2002.Google Scholar
[14]Pillay, A., First order topological structures and theories, this Journal, vol. 52 (1987), no. 3, pp. 763–778.Google Scholar
[15]Pop, F., Embedding problems over large fields, Annals of Mathematics (2), vol. 144 (1996), no. 1, pp. 1–34.CrossRefGoogle Scholar
[16]Scanlon, T., A model complete theory of valued D-fields, this Journal, vol. 65 (2000), pp. 323–352.Google Scholar
[17]Scanlon, T., Quantifier elimination for the relative Frobenius, Fields Institute Communications, vol. 33 (2003), pp. 323–359.Google Scholar
[18]van den Dries, L., Dimension of definable sets, algebraic boundedness and henselian fields, Annals of Pure and Applied Logic, vol. 45 (1989), pp. 189–209.CrossRefGoogle Scholar
[19]Wilkie, A.J., Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function, Journal of the American Mathematical Society, vol. 9 (1996), no. 4, pp. 1051–1094.CrossRefGoogle Scholar