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Stabilité polynômiale des corps différentiels

Published online by Cambridge University Press:  12 March 2014

Natacha Portier
Natacha Portier*
Affiliation:
Institut Girard Desargues- Upres-A 5028 Du CNRS, Université Claude Bernard Lyon-I, Bâtiment Du Doyen Jean Braconnier (101), 43, Boulevard Du 11 Novembre 1918, 69 622 Villeurbanne Cedex, France E-mail: [email protected]
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Abstract

A notion of complexity for an arbitrary structure was defined in the book of Poizat Les petits cailloux (1995): we can define P and NP problems over a differential field K. Using the Witness Theorem of Blum et al., we prove the P-stability of the theory of differential fields: a P problem over a differential field K is still P when restricts to a sub-differential field k of K. As a consequence, if P = NP over some differentially closed field K, then P = NP over any differentially closed field and over any algebraically closed field.

Keywords

ComplexityDifferential FieldDefinissability of TypesStability
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 803 - 816
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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