Stabilité polynômiale Des corps différentiels

Journal of Symbolic Logic 64 (2):803-816 (1999)
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 Complexity   Differential Field   Definissability of Types   Stability
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