Plongement dense d'un corps ordonné dans sa clôture réelle

Abstract

AbstractWe study the structures (K ⊂ Kr), where K is an ordered field and Kr its real closure, in the language of ordered fields with an additional unary predicate for the subfield K. Two such structures (K ⊂ Kr) and (L ⊂ Lr) are not necessarily elementary equivalent when K and L are. But with some saturation assumption on K and L, then the two structures become equivalent, and we give a description of the complete theory.