Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 64, Issue 2 (1999), 803-816.
Stabilite Polynomiale des Corps Differentiels
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.
J. Symbolic Logic, Volume 64, Issue 2 (1999), 803-816.
First available in Project Euclid: 6 July 2007
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Portier, Natacha. Stabilite Polynomiale des Corps Differentiels. J. Symbolic Logic 64 (1999), no. 2, 803--816. https://projecteuclid.org/euclid.jsl/1183745811