Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 64, Issue 2 (1999), 803-816.
Stabilite Polynomiale des Corps Differentiels
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
