Abstract
Blum et al. (1989) showed the existence of a NP-complete problem over the real closed fields in the framework of their theory of computation over the reals. This allows to ask for the P≠NP question over real closed fields. Here we show that P≠NP over a real closed extension of the reals implies P≠NP over the reals. We also discuss the converse. This leads to define some subclasses of P/poly. Finally we show that the transfer result about P≠NP is a part of a very abstract result.
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