Journal of Symbolic Logic

Stabilite Polynomiale des Corps Differentiels

Natacha Portier

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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.

Article information

Source
J. Symbolic Logic, Volume 64, Issue 2 (1999), 803-816.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745811

Mathematical Reviews number (MathSciNet)
MR1777788

Zentralblatt MATH identifier
0939.03040

JSTOR
links.jstor.org

Keywords
Complexity Differential Field Definissability of Types Stability

Citation

Portier, Natacha. Stabilite Polynomiale des Corps Differentiels. J. Symbolic Logic 64 (1999), no. 2, 803--816. https://projecteuclid.org/euclid.jsl/1183745811


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